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Math Problems
Grade 6
One-step inequalities: word problems
The electric charge of magnesium is
2
2
2
. The electric charge of potassium is
1
1
1
. Write an inequality that correctly compares the charges.
\newline
Which one of the following descriptions is correct? Choose
1
1
1
answer:
\newline
(Choice A) Magnesium's charge is more positive than potassium's charge.
\newline
(Choice B) Potassium's charge is more positive than magnesium's charge.
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Hunter, a meteorologist, keeps track of the amount of rain each year relative to the amount of rain in
1900
1900
1900
. Two years of data are shown in the table below.
\newline
Year Amount of rain relative to
1900
1900
1900
(in cm)
\newline
1945
1945
1945
−
19
-19
−
19
\newline
1946
1946
1946
36
36
36
\newline
Drag the white cards onto the gray rectangle to write an inequality that correctly compares the relative amounts of rain.
\newline
−
19
-19
−
19
<
<
<
36
36
36
\newline
Which one of the following descriptions is correct? Choose
1
1
1
answer:
\newline
Choose
1
1
1
answer:
\newline
(Choice A) There was less rain in
1946
1946
1946
than in
1945
1945
1945
.
\newline
A There was less rain in
1946
1946
1946
than in
1945
1945
1945
.
\newline
(Choice B) There was less rain in
1945
1945
1945
than in
1946
1946
1946
.
\newline
B There was less rain in
1945
1945
1945
than in
1946
1946
1946
.
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Jake is younger than Sophie. Sophie is
14
14
14
years old. Write an inequality that compares Jake's age in years,
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Jake is younger than Sophie. Sophie is
14
14
14
years old. Write an inequality that compares Jake's age in years,
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lazing!
\newline
week
\newline
streak
\newline
Quiz
3
3
3
\newline
Jake is younger than Sophie. Sophie is
14
14
14
years old.
\newline
Write an inequality that compares Jake's age in years,
j
j
j
, to Sophie's age
□
\square
□
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The formula for the length of the hypotenuse in a right triangle is
a
2
+
b
2
\sqrt{a^2+b^2}
a
2
+
b
2
where
a
a
a
and
b
b
b
are the lengths of the triangle's sides (this formula is derived from the Pythagorean theorem). From the side, a certain ramp has a right-triangular shape. Its height is
30
30
30
centimeters and its horizontal length is
3
3
3
meters. What calculation will give us the estimated length of the ramp in meters? Choose
1
1
1
answer: Choose
1
1
1
answer: (Choice A)
3
0
2
10
0
2
+
3
2
\sqrt{\dfrac{30^2}{100^2}+3^2}
10
0
2
3
0
2
+
3
2
A
3
0
2
10
0
2
+
3
2
\sqrt{\dfrac{30^2}{100^2}+3^2}
10
0
2
3
0
2
+
3
2
(Choice B, Checked)
3
0
2
+
3
2
⋅
10
0
2
\sqrt{30^2+3^2\cdot 100^2}
3
0
2
+
3
2
⋅
10
0
2
B
3
0
2
+
3
2
⋅
10
0
2
\sqrt{30^2+3^2\cdot 100^2}
3
0
2
+
3
2
⋅
10
0
2
(Choice C)
3
0
2
⋅
10
0
2
+
3
2
\sqrt{30^2\cdot 100^2+3^2}
3
0
2
⋅
10
0
2
+
3
2
C
3
0
2
⋅
10
0
2
+
3
2
\sqrt{30^2\cdot 100^2+3^2}
3
0
2
⋅
10
0
2
+
3
2
(Choice D)
3
0
2
+
3
2
10
0
2
\sqrt{30^2+\dfrac{3^2}{100^2}}
3
0
2
+
10
0
2
3
2
D
3
0
2
+
3
2
10
0
2
\sqrt{30^2+\dfrac{3^2}{100^2}}
3
0
2
+
10
0
2
3
2
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A zoo has a limited daily supply of leaves to feed elephants and giraffes. Every day, each giraffe eats the same amount of leaves, and each elephant eats
47
kg
47\text{ kg}
47
kg
of leaves. Let
E
E
E
represent the number of elephants and
G
G
G
represent the number of giraffes that the zoo can feed with its daily supply of leaves.
47
E
+
24
G
≤
500
47E+24G \leq 500
47
E
+
24
G
≤
500
According to the inequality, what is the zoo's daily supply of leaves, and how many
kg
\text{kg}
kg
of leaves does each giraffe eat per day?
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The Jacksons and the Simpsons were competing in the final leg of the Amazing Race, which was
240
240
240
kilometers long.
\newline
In their race to the finish, the Jacksons immediately took off traveling at a average speed of
v
v
v
kilometers per hour. The Simpsons' start was delayed by an hour. When they eventually took off, they traveled at an average speed that was
40
40
40
kilometers per hour faster than the Jacksons' speed. Sadly for them, that didn't help, and the Jacksons won.
\newline
Write an inequality in terms of
v
v
v
that models the situation.
□
\square
□
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Renna pushes the elevator button, but the elevator does not move. The mass limit for the elevator is
450
450
450
kilograms (
kg
\text{kg}
kg
), but Renna and her load of identical packages mass a total of
620
kg
620\,\text{kg}
620
kg
. Each package has a mass of
37.4
kg
37.4\,\text{kg}
37.4
kg
. Write an inequality to determine the number of packages,
p
p
p
, Renna could remove from the elevator to meet the mass requirement.
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The graph of
y
=
x
3
y=\sqrt[3]{x}
y
=
3
x
is shown below.
2
\small{2}
2
4
\small{4}
4
6
\small{6}
6
8
\small{8}
8
-
4
\small{\llap{-}4}
-
4
-
6
\small{\llap{-}6}
-
6
-
8
\small{\llap{-}8}
-
8
2
\small{2}
2
4
\small{4}
4
6
\small{6}
6
8
\small{8}
8
-
4
\small{\llap{-}4}
-
4
-
6
\small{\llap{-}6}
-
6
-
8
\small{\llap{-}8}
-
8
y
y
y
x
x
x
Which of the following is the graph of
y
=
5
−
x
3
+
4
y=\sqrt[3]{5-x}+4
y
=
3
5
−
x
+
4
? Choose
1
1
1
answer: Choose
1
1
1
answer: (Choice A) A cube root function graph on an x y coordinate plane. It has been shifted up four, to the left five spaces, and horizontally reflected.
2
\small{2}
2
4
\small{4}
4
6
\small{6}
6
8
\small{8}
8
-
4
\small{\llap{-}4}
-
4
-
6
\small{\llap{-}6}
-
6
-
8
\small{\llap{-}8}
-
8
2
\small{2}
2
4
\small{4}
4
6
\small{6}
6
8
\small{8}
8
-
4
\small{\llap{-}4}
-
4
-
6
\small{\llap{-}6}
-
6
-
8
\small{\llap{-}8}
-
8
y
y
y
x
x
x
o
r
m
a
l
s
i
z
e
A
ormalsize{\text{A}}
or
ma
l
s
i
ze
A
A A cube root function graph on an x y coordinate plane. It has been shifted up four, to the left five spaces, and horizontally reflected.
2
\small{2}
2
4
\small{4}
4
6
\small{6}
6
8
\small{8}
8
-
4
\small{\llap{-}4}
-
4
-
6
\small{\llap{-}6}
-
6
-
8
\small{\llap{-}8}
-
8
2
\small{2}
2
4
\small{4}
4
6
\small{6}
6
8
\small{8}
8
-
4
\small{\llap{-}4}
-
4
-
6
\small{\llap{-}6}
-
6
-
8
\small{\llap{-}8}
-
8
y
y
y
x
x
x
o
r
m
a
l
s
i
z
e
A
ormalsize{\text{A}}
or
ma
l
s
i
ze
A
(Choice B) A cube root function graph on an x y coordinate plane. It has been shifted up four, to the right five spaces, and horizontally reflected.
2
\small{2}
2
4
\small{4}
4
6
\small{6}
6
8
\small{8}
8
-
4
\small{\llap{-}4}
-
4
-
6
\small{\llap{-}6}
-
6
-
8
\small{\llap{-}8}
-
8
2
\small{2}
2
4
\small{4}
4
6
\small{6}
6
8
\small{8}
8
-
4
\small{\llap{-}4}
-
4
-
6
\small{\llap{-}6}
-
6
-
8
\small{\llap{-}8}
-
8
y
y
y
x
x
x
o
r
m
a
l
s
i
z
e
B
ormalsize{\text{B}}
or
ma
l
s
i
ze
B
B A cube root function graph on an x y coordinate plane. It has been shifted up four, to the right five spaces, and horizontally reflected.
2
\small{2}
2
4
\small{4}
4
6
\small{6}
6
8
\small{8}
8
-
4
\small{\llap{-}4}
-
4
-
6
\small{\llap{-}6}
-
6
-
8
\small{\llap{-}8}
-
8
2
\small{2}
2
4
\small{4}
4
6
\small{6}
6
8
\small{8}
8
-
4
\small{\llap{-}4}
-
4
-
6
\small{\llap{-}6}
-
6
-
8
\small{\llap{-}8}
-
8
y
y
y
x
x
x
o
r
m
a
l
s
i
z
e
B
ormalsize{\text{B}}
or
ma
l
s
i
ze
B
(Choice C) A cube root function graph on an x y coordinate plane. It has been shifted up four and to the left five spaces.
2
\small{2}
2
4
\small{4}
4
6
\small{6}
6
8
\small{8}
8
-
4
\small{\llap{-}4}
-
4
-
6
\small{\llap{-}6}
-
6
-
8
\small{\llap{-}8}
-
8
2
\small{2}
2
4
\small{4}
4
6
\small{6}
6
8
\small{8}
8
-
4
\small{\llap{-}4}
-
4
-
6
\small{\llap{-}6}
-
6
-
8
\small{\llap{-}8}
-
8
y
y
y
x
x
x
o
r
m
a
l
s
i
z
e
C
ormalsize{\text{C}}
or
ma
l
s
i
ze
C
C A cube root function graph on an x y coordinate plane. It has been shifted up four and to the left five spaces.
2
\small{2}
2
4
\small{4}
4
6
\small{6}
6
8
\small{8}
8
-
4
\small{\llap{-}4}
-
4
-
6
\small{\llap{-}6}
-
6
-
8
\small{\llap{-}8}
-
8
2
\small{2}
2
4
\small{4}
4
6
\small{6}
6
8
\small{8}
8
-
4
\small{\llap{-}4}
-
4
-
6
\small{\llap{-}6}
-
6
-
8
\small{\llap{-}8}
-
8
y
y
y
x
x
x
o
r
m
a
l
s
i
z
e
C
ormalsize{\text{C}}
or
ma
l
s
i
ze
C
(Choice D) A cube root function graph on an x y coordinate plane. It has been shifted up four and to the right five spaces.
2
\small{2}
2
4
\small{4}
4
6
\small{6}
6
8
\small{8}
8
-
4
\small{\llap{-}4}
-
4
-
6
\small{\llap{-}6}
-
6
-
8
\small{\llap{-}8}
-
8
2
\small{2}
2
4
\small{4}
4
6
\small{6}
6
8
\small{8}
8
-
4
\small{\llap{-}4}
-
4
-
6
\small{\llap{-}6}
-
6
-
8
\small{\llap{-}8}
-
8
y
y
y
x
x
x
o
r
m
a
l
s
i
z
e
D
ormalsize{\text{D}}
or
ma
l
s
i
ze
D
D A cube root function graph on an x y coordinate plane. It has been shifted up four and to the right five spaces.
2
\small{2}
2
4
\small{4}
4
6
\small{6}
6
8
\small{8}
8
-
4
\small{\llap{-}4}
-
4
-
6
\small{\llap{-}6}
-
6
-
8
\small{\llap{-}8}
-
8
2
\small{2}
2
4
\small{4}
4
6
\small{6}
6
8
\small{8}
8
-
4
\small{\llap{-}4}
-
4
-
6
\small{\llap{-}6}
-
6
-
8
\small{\llap{-}8}
-
8
y
y
y
x
x
x
o
r
m
a
l
s
i
z
e
D
ormalsize{\text{D}}
or
ma
l
s
i
ze
D
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Roselyn is driving to visit her family, who live
150
150
150
kilometers away. Her average speed is
60
60
60
kilometers per hour. The car's tank has
20
20
20
liters of fuel at the beginning of the drive, and its fuel efficiency is
6
6
6
kilometers per liter. Fuel costs
0.60
0.60
0.60
dollars per liter. How long can Roselyn drive before she runs out of fuel? hours
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The double number line shows that Jéssica lives
\newline
48
km
48\,\text{km}
48
km
from the capitol.
\newline
A double number line with
2
2
2
tick marks. The line labeled Distance, kilometers, reads from left to right:
0
0
0
,
48
48
48
. The line labeled Percentage, reads from left to right:
0
0
0
percent,
100
100
100
percent.
\newline
0
0
0
\newline
48
48
48
\newline
48
48
48
\newline
0
%
0\%
0%
\newline
100
%
100\%
100%
\newline
100
%
100\%
100%
\newline
Complete the table to show different percentages of the distance.
\newline
Distance (
\newline
km
\text{km}
km
) Percentage
\newline
48
48
48
\newline
%
\%
%
of
\newline
48
km
48\,\text{km}
48
km
\newline
0
0
0
1
1
1
\newline
%
\%
%
of
\newline
48
km
48\,\text{km}
48
km
\newline
0
0
0
4
4
4
\newline
%
\%
%
of
\newline
48
km
48\,\text{km}
48
km
\newline
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Which expressions are equivalent to
\newline
7
−
2
⋅
7
6
7^{-2}\cdot 7^6
7
−
2
⋅
7
6
? Choose
2
2
2
answers: Choose
2
2
2
answers:
\newline
(Choice A)
7
2
7
−
2
\dfrac{7^2}{7^{-2}}
7
−
2
7
2
\newline
(Choice B, Checked)
7
6
7
−
2
\dfrac{7^6}{7^{-2}}
7
−
2
7
6
\newline
(Choice C, Checked)
7
−
12
7^{-12}
7
−
12
\newline
(Choice D)
(
7
2
)
2
(7^2)^2
(
7
2
)
2
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A lake near the Arctic Circle is covered by a
[
2
]
[2]
[
2
]
-meter-thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. After
[
3
]
[3]
[
3
]
weeks, the sheet is only
[
1.25
]
[1.25]
[
1.25
]
meters thick. Let
[
y
]
[y]
[
y
]
represent the ice sheet's thickness (in meters) after
[
x
]
[x]
[
x
]
weeks. Which of the following information about the graph of the relationship is given? Choose
1
1
1
answer: Choose
1
1
1
answer:
\newline
(Choice A) Slope and
\newline
[x]-intercept
\newline
(Choice B) Slope and
\newline
[y]-intercept
\newline
(Choice C) Slope and a point that is not an intercept
\newline
(Choice D)
\newline
[x]-intercept and
\newline
[y]-intercept
\newline
(Choice E)
\newline
[y]-intercept and a point that is not an intercept
\newline
(Choice F) Two points that are not intercepts
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The two-way table of row relative frequencies below shows data on nationality and eye color. Brown or hazel eyes
[
0.48
]
[0.48]
[
0.48
]
Blue or green eyes
[
0.50
]
[0.50]
[
0.50
]
Other
[
0.02
]
[0.02]
[
0.02
]
Row total English
[
1.00
]
[1.00]
[
1.00
]
German
[
0.47
]
[0.47]
[
0.47
]
[
0.52
]
[0.52]
[
0.52
]
[
0.01
]
[0.01]
[
0.01
]
[
1.00
]
[1.00]
[
1.00
]
Italian
[
0.80
]
[0.80]
[
0.80
]
[
0.18
]
[0.18]
[
0.18
]
[
0.02
]
[0.02]
[
0.02
]
[
1.00
]
[1.00]
[
1.00
]
Based on the data, which of the following statements must be true? Choose
1
1
1
answer: Choose
1
1
1
answer:
\newline
A) There are the same number of English people and Italian people with other eye colors.
\newline
B) Italians are more likely to have brown or hazel eyes than Germans are.
\newline
C) A German person is more likely to have brown or hazel eyes than to have blue or green eyes.
\newline
D) A person with brown or hazel eyes is least likely to be German.
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It takes
31
31
31
employees and
e
x
t
e
x
t
d
o
l
l
a
r
7500
ext{ extdollar}7500
e
x
t
e
x
t
d
o
ll
a
r
7500
to build a car, and it takes
19
19
19
employees and
e
x
t
e
x
t
d
o
l
l
a
r
4300
ext{ extdollar}4300
e
x
t
e
x
t
d
o
ll
a
r
4300
to build a motorcycle. Genghis Motors wants to spend more than
e
x
t
e
x
t
d
o
l
l
a
r
84000
ext{ extdollar}84000
e
x
t
e
x
t
d
o
ll
a
r
84000
to build cars and motorbikes using at most
706
706
706
employees. Let
C
C
C
denote the number of cars they build and
M
M
M
the number of motorbikes they build. Write an inequality that represents the condition based on the number of employees.
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A cupcake requires
35
35
35
grams of sugar and
50
50
50
grams of flour, and a muffin requires
30
30
30
grams of sugar and
65
65
65
grams of flour. Shawna needs to use up at least
460
460
460
grams of sugar to make cupcakes and muffins, and she wants to use at most
970
970
970
grams of flour. Let
C
C
C
denote the number of cupcakes she makes and
M
M
M
the number of muffins she makes. Write an inequality that represents the condition based on the number of grams of sugar.
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Chiamaka is
x
x
x
from the university and drives
y
y
y
closer every hour. Valente is
z
z
z
from the university and drives
w
w
w
closer every hour. Let
t
t
t
represent the time, in hours, since Chiamaka and Valente started driving toward the university. Complete the inequality to represent the times when Valente is closer than Chiamaka to the university.
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Max tried to solve
7
v
+
19
=
2
(
10
v
+
3
)
7v + 19 = 2(10v + 3)
7
v
+
19
=
2
(
10
v
+
3
)
:
\newline
7
v
+
19
=
20
v
+
3
7v + 19 = 20v + 3
7
v
+
19
=
20
v
+
3
{Step
1
1
1
}
\newline
19
=
13
v
+
3
19 = 13v + 3
19
=
13
v
+
3
{Step
2
2
2
}
\newline
16
=
13
v
16 = 13v
16
=
13
v
{Step
3
3
3
}
\newline
16
13
=
v
\frac{16}{13} = v
13
16
=
v
{Step
4
4
4
}
\newline
Did Max solve the equation correctly?
\newline
(A)Yes, Max solved the equation correctly.
\newline
(B)No, Max made a mistake in step
1
1
1
. He didn't apply the distributive property correctly.
\newline
(C)No, Max made a mistake in step
2
2
2
. He didn't combine the terms with
v
v
v
on the left side of the equation.
\newline
(D)No, Max made a mistake in step
4
4
4
. He didn't apply the division property of equality correctly.
Get tutor help
Leah is making a square wooden picture frame for woodworking class. After dividing a piece of wood she wants to use into
4
4
4
equal pieces, Leah figures each side of her frame can be at most
12
12
12
inches long.
\newline
Let
x
x
x
represent the perimeter of the picture frame. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
x
4
≤
12
\frac{x}{4} \leq 12
4
x
≤
12
\newline
(B)
x
4
<
12
\frac{x}{4} < 12
4
x
<
12
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
The perimeter of the picture frame will be at most
_
_
_
\_\_\_
___
inches.
Get tutor help
A local ice cream shop has a parking lot with enough space for
18
18
18
cars. There are
7
7
7
cars in the parking lot right now.
\newline
Let
x
x
x
represent how many more cars can park in the lot. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
x
+
7
≤
18
x + 7 \leq 18
x
+
7
≤
18
\newline
(B)
x
+
7
≥
18
x + 7 \geq 18
x
+
7
≥
18
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
Up to ___ more cars can park in the lot.
Get tutor help
Hector is building a metal sculpture in the shape of an equilateral triangle. After he divides a metal bar into
3
3
3
equal pieces, Hector figures each side of the triangular sculpture can be at most
9
9
9
feet long.
\newline
Let
x
x
x
represent the perimeter of the triangular sculpture. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
x
3
\frac{x}{3}
3
x
≤
9
\leq 9
≤
9
\newline
(B)
x
3
\frac{x}{3}
3
x
<
9
< 9
<
9
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
The perimeter of the triangular sculpture can be at most
_
_
_
\_\_\_
___
feet.
Get tutor help
Anne picked out
3
3
3
board games from her cabinet to take to a game night with her friends. She still has more than
10
10
10
board games in the cabinet, so she thinks she could bring a few more.
\newline
Let
x
x
x
represent how many board games were in Anne's cabinet to start. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
x
−
3
>
10
x - 3 > 10
x
−
3
>
10
\newline
(B)
x
−
3
≥
10
x - 3 \geq 10
x
−
3
≥
10
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
There were more than ____ board games in Anne's cabinet to start.
Get tutor help
Ms. Estrada plans to take
36
36
36
chocolate chip cookies to sell at a bake sale. She wants to bake enough to keep at least
24
24
24
cookies for her cookie jar at home.
\newline
Let
x
x
x
represent how many chocolate chip cookies Ms. Estrada will bake. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
x
−
36
≤
24
x - 36 \leq 24
x
−
36
≤
24
\newline
(B)
x
−
36
≥
24
x - 36 \geq 24
x
−
36
≥
24
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
Ms. Estrada will bake at least ____ chocolate chip cookies.
Get tutor help
It takes at least
9
9
9
players to form a baseball team. So far,
5
5
5
players have joined the Blue Jays baseball team.
\newline
Let
x
x
x
represent how many more players need to join. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
5
+
x
≥
9
5 + x \geq 9
5
+
x
≥
9
\newline
(B)
5
+
x
>
9
5 + x > 9
5
+
x
>
9
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
At least ____ more players need to join.
Get tutor help
A high school will only offer a pottery class next year if at least
15
15
15
students sign up. So far,
9
9
9
students have signed up for the pottery class.
\newline
Let
x
x
x
represent how many more students need to sign up. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
9
+
x
≥
15
9 + x \geq 15
9
+
x
≥
15
\newline
(B)
9
+
x
>
15
9 + x > 15
9
+
x
>
15
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
At least
_
_
_
\_\_\_
___
more students need to sign up.
Get tutor help
Mr. Brown is splitting his students into groups to give presentations about novels they read. He wants each group to have
4
4
4
students. There are fewer than
24
24
24
students in class today, so Mr. Brown can't make as many full groups as he had planned.
\newline
Let
x
x
x
represent how many full groups Mr. Brown can make. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
4
x
>
24
4x > 24
4
x
>
24
\newline
(B)
4
x
<
24
4x < 24
4
x
<
24
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
Mr. Brown can make fewer than ____ full groups.
Get tutor help
After Simon fully charges his electric car, he can drive for up to
350
350
350
miles before it runs out of battery. Simon's car was fully charged this morning, and he has driven
140
140
140
miles since then.
\newline
Let
x
x
x
represent how many more miles Simon can drive without running out of battery. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
140
+
x
≥
350
140 + x \geq 350
140
+
x
≥
350
\newline
(B)
140
+
x
≤
350
140 + x \leq 350
140
+
x
≤
350
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
Simon can drive up to
_
_
_
\_\_\_
___
more miles before running out of battery.
Get tutor help
Mr. Dawson is making a grocery budget for the month of April. He plans to split the budget equally among
4
4
4
shopping trips. To stay under budget, Mr. Dawson figures he should spend less than
$
180
\$180
$180
each trip.
\newline
Let
x
x
x
represent how much Mr. Dawson wants to spend on groceries in April. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
x
4
<
180
\frac{x}{4} < 180
4
x
<
180
\newline
(B)
x
4
>
180
\frac{x}{4} > 180
4
x
>
180
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
Mr. Dawson wants to spend less than
$
_
_
_
\$\_\_\_
$___
on groceries in April.
Get tutor help
Mary plans to buy
5
5
5
tickets to go to an orchestra concert with her friends. She expects to spend at least
$
90
\$90
$90
on the tickets.
\newline
Let
x
x
x
represent how much Mary expects each ticket to cost. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
5
x
≥
90
5x \geq 90
5
x
≥
90
\newline
(B)
5
x
<
90
5x < 90
5
x
<
90
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
Mary expects each ticket to cost at least
$
_
\$\_
$_
.
Get tutor help
After Simon fully charges his electric car, he can drive for up to
350
350
350
miles before it runs out of battery. Simon's car was fully charged this morning, and he has driven
140
140
140
miles since then.
\newline
Let
x
x
x
represent how many more miles Simon can drive without running out of battery. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
140
+
x
≤
350
140 + x \leq 350
140
+
x
≤
350
\newline
(B)
140
+
x
≥
350
140 + x \geq 350
140
+
x
≥
350
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
Simon can drive up to ____ more miles before running out of battery.
Get tutor help
Kate's Cupcakes sells cupcakes in boxes of
4
4
4
. Depending on the type of cupcake, a box can cost at most
$
20
\$20
$20
.
\newline
Let
x
x
x
represent how much each cupcake costs. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
4
x
≥
20
4x \geq 20
4
x
≥
20
\newline
(B)
4
x
≤
20
4x \leq 20
4
x
≤
20
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
Each cupcake costs at most
$
\$
$
___.
Get tutor help
Kate's Cupcakes sells cupcakes in boxes of
4
4
4
. Depending on the type of cupcake, a box can cost at most
$
20
\$20
$20
.
\newline
Let
x
x
x
represent how much each cupcake costs. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
4
x
≤
20
4x \leq 20
4
x
≤
20
\newline
(B)
4
x
≥
20
4x \geq 20
4
x
≥
20
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
Each cupcake costs at most
$
\$
$
___.
Get tutor help
Coach Kirby is forming dodgeball teams from students in her physical education class. She wants teams that each have
6
6
6
students. There are fewer than
48
48
48
students in the class, so Coach Kirby can't form as many full teams as she wants.
\newline
Let
x
x
x
represent how many full teams Coach Kirby can form. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
6
x
>
48
6x > 48
6
x
>
48
\newline
(B)
6
x
<
48
6x < 48
6
x
<
48
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
Coach Kirby can form fewer than ____ full teams.
Get tutor help
Estelle bought
3
3
3
pineapples to cut up and serve on a fruit platter. The pineapples each cost the same amount, and they cost less than
$
12
\$12
$12
in all.
\newline
Let
x
x
x
represent how much each pineapple cost. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
3
x
>
12
3x > 12
3
x
>
12
\newline
(B)
3
x
<
12
3x < 12
3
x
<
12
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
Each pineapple cost less than
$
\$
$
_
_
_
\_\_\_
___
.
Get tutor help
Laura is drawing a rectangle. The width will be
3
centimeters
3\,\text{centimeters}
3
centimeters
, and the area will be at least
18
square centimeters
18\,\text{square centimeters}
18
square centimeters
. Let
x
x
x
represent the length of the rectangle. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
3
x
≤
18
3x \leq 18
3
x
≤
18
\newline
(B)
3
x
≥
18
3x \geq 18
3
x
≥
18
\newline
Solve the inequality. Then, complete the sentence to describe the solution. The rectangle will be at least
_
_
_
_
\_\_\_\_
____
centimeters long.
Get tutor help
A shuttle bus to Willow Creek Mall has enough seats for
21
21
21
people to ride. Right now, there are
12
12
12
people on the bus.
\newline
Let
x
x
x
represent how many more people can ride on the bus. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
12
+
x
≥
21
12 + x \geq 21
12
+
x
≥
21
\newline
(B)
12
+
x
≤
21
12 + x \leq 21
12
+
x
≤
21
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
Up to ____ more people can ride on the bus.
Get tutor help
Kendra is drawing a rectangle. The length will be
4
4
4
inches, and the area will be at least
12
12
12
square inches.
\newline
Let
x
x
x
represent the width of the rectangle. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
4
x
≤
12
4x \leq 12
4
x
≤
12
\newline
(B)
4
x
≥
12
4x \geq 12
4
x
≥
12
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
The rectangle will be at least
_
_
_
\_\_\_
___
inches wide.
Get tutor help
Leah is making a square wooden picture frame for woodworking class. After dividing a piece of wood she wants to use into
4
4
4
equal pieces, Leah figures each side of her frame can be at most
12
12
12
inches long.
\newline
Let
x
x
x
represent the perimeter of the picture frame. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
x
4
<
12
\frac{x}{4} < 12
4
x
<
12
\newline
(B)
x
4
≤
12
\frac{x}{4} \leq 12
4
x
≤
12
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
The perimeter of the picture frame will be at most
_
_
_
\_\_\_
___
inches.
Get tutor help
In the first week of her school's fundraiser, Julie sold
6
6
6
items. By the end of the fundraiser, Julie had earned a beach ball as a prize for selling more than
20
20
20
items.
\newline
Let
x
x
x
represent how many more items Julie sold after the first week of the fundraiser. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
6
+
x
≥
20
6 + x \geq 20
6
+
x
≥
20
\newline
(B)
6
+
x
>
20
6 + x > 20
6
+
x
>
20
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
Julie sold more than ____ items after the first week of the fundraiser.
Get tutor help
Turner made spiced apple cider for a holiday party and divided it evenly among
12
12
12
mugs. Each mug had more than
10
10
10
fluid ounces of apple cider.
\newline
Let
x
x
x
represent how much apple cider Turner made. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
x
12
≥
10
\frac{x}{12} \geq 10
12
x
≥
10
\newline
(B)
x
12
>
10
\frac{x}{12} > 10
12
x
>
10
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
Turner made more than ____ fluid ounces of apple cider.
Get tutor help
Naomi had a blast at the water park, even though she was
3
3
3
inches too short to ride the biggest slide, The Water Slinger. Naomi is
49
49
49
inches tall.
\newline
Let
h
h
h
represent the minimum height for The Water Slinger. Which equation models the problem?
\newline
Choices:
\newline
(A)
h
−
3
=
49
h - 3 = 49
h
−
3
=
49
\newline
(B)
h
+
3
=
49
h + 3 = 49
h
+
3
=
49
\newline
Solve this equation to find the minimum height for The Water Slinger.
\newline
____ inches
\newline
Get tutor help
A local theater sells both regular priced admission tickets for their evening movies and reduced priced admission tickets for their earrier matinee shows. Over the course of one business day, the theater earned
$
6
,
721
\$6,721
$6
,
721
in revenue and sold
558
558
558
total tickets. Find how many of each type of ticket, was sold if regular price admission is
$
13.50
\$13.50
$13.50
and tickets for matinee times are
$
6.50
\$6.50
$6.50
.
Get tutor help
A crayon company recently changed its labels. It currently has a total of
814
814
814
crayons in stock,
156
156
156
of which have the new label. About how many crayons with the old label does the company have in stock? Choose the better estimate.
\newline
Choices:
\newline
(A)
600
600
600
\newline
(B)
1
,
600
1,600
1
,
600
Get tutor help
Sophie tried to evaluate an expression. Here is her work:
\newline
9
2
÷
3
2
×
2
+
7
×
6
9^2 \div 3^2 \times 2 + 7 \times 6
9
2
÷
3
2
×
2
+
7
×
6
\newline
81
÷
9
×
2
+
7
×
6
81 \div 9 \times 2 + 7 \times 6
81
÷
9
×
2
+
7
×
6
{Step
1
1
1
}
\newline
9
×
2
+
7
×
6
9 \times 2 + 7 \times 6
9
×
2
+
7
×
6
{Step
2
2
2
}
\newline
18
+
7
×
6
18 + 7 \times 6
18
+
7
×
6
{Step
3
3
3
}
\newline
25
×
7
25 \times 7
25
×
7
{Step
4
4
4
}
\newline
175
175
175
{Step
5
5
5
}
\newline
Is Sophie's work correct?
\newline
(A)No, Sophie made a mistake going from Step
1
1
1
to Step
2
2
2
. Sophie should have multiplied
9
9
9
and
2
2
2
before dividing. The order of operations says to multiply before you divide.
\newline
(B)No, Sophie made a mistake going from Step
3
3
3
to Step
4
4
4
. Sophie should have multiplied
7
7
7
and
6
6
6
before adding. The order of operations says to multiply before you add.
\newline
(C)Yes, Sophie's work is correct.
Get tutor help
5
5
5
markers cost
$
6.55
\$6.55
$6.55
. Which equation would help determine the cost of
4
4
4
markers? Choose
1
1
1
answer:
\newline
(A)
4
5
=
$
6.55
x
\frac{4}{5}=\frac{\$6.55}{x}
5
4
=
x
$6.55
\newline
(B)
4
$
6.55
=
x
5
\frac{4}{\$6.55}=\frac{x}{5}
$6.55
4
=
5
x
\newline
(C)
5
4
=
x
$
6.55
\frac{5}{4}=\frac{x}{\$6.55}
4
5
=
$6.55
x
\newline
(D)
4
$
6.55
4\quad\$6.55
4
$6.55
Get tutor help
Requires
2
2
2
ice-cream scoops and
6
6
6
strawberries. Ramses wants to make sundaes and milkshakes with at most
25
25
25
ice-cream scoops and
37
37
37
strawberries. Let
S
S
S
denote the number of sundaes he makes and
M
M
M
the number of milkshakes he makes. Write an inequality that represents the condition based on the number of strawberries.
Get tutor help
A right rectangular prism has length
2
1
2
2\frac{1}{2}
2
2
1
yd, width
1
1
2
1\frac{1}{2}
1
2
1
yd, and height
3
1
2
3\frac{1}{2}
3
2
1
yd. You use cubes with fractional edge length
(
1
2
)
(\frac{1}{2})
(
2
1
)
each of the length, width, and height of the prism? Find the volume. How many cubes are there for each of the length, width, and height of the prism? The length has
□
\square
□
cubes, the width has
□
\square
□
cubes, and the height has
□
\square
□
cubes.
Get tutor help
Reggie has picked out
4
4
4
shirts from his closet to donate. He still has more than
15
15
15
shirts left in his closet, so he thinks he should donate some more.
\newline
Let
x
x
x
represent how many shirts were in Reggie's closet to start. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
x
−
4
>
15
x - 4 > 15
x
−
4
>
15
\newline
(B)
x
−
4
≥
15
x - 4 \geq 15
x
−
4
≥
15
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
There were more than ____ shirts in Reggie's closet to start.
Get tutor help
At Cindy's Sweet Treats, cookies are packaged in boxes of
8
8
8
. Depending on the cookie flavor, the most a box can cost is
$
16
\$16
$16
. Let
x
x
x
represent how much each cookie costs. Which inequality describes the problem?
\newline
Choices:
\newline
(A)
8
x
≤
16
8x \leq 16
8
x
≤
16
\newline
(B)
8
x
≥
16
8x \geq 16
8
x
≥
16
\newline
Solve the inequality. Then, complete the sentence to describe the solution.
\newline
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