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Let’s check out your problem:
Solve for
x
x
x
.
\newline
x
(
x
−
3
)
≥
0
x(x - 3) \geq 0
x
(
x
−
3
)
≥
0
\newline
Write a compound inequality like 1 < x < 3 or like x < 1 or x > 3.______
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Home
Math Problems
Algebra 2
Solve quadratic inequalities
Full solution
Q.
Solve for
x
x
x
.
\newline
x
(
x
−
3
)
≥
0
x(x - 3) \geq 0
x
(
x
−
3
)
≥
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.______
Divide Intervals:
Divide the number line into intervals using the zeros:
(
−
∞
,
0
)
(-\infty, 0)
(
−
∞
,
0
)
,
(
0
,
3
)
(0, 3)
(
0
,
3
)
,
(
3
,
∞
)
(3, \infty)
(
3
,
∞
)
.
Test Interval
(
−
∞
,
0
)
(-\infty, 0)
(
−
∞
,
0
)
:
Test the interval
(
−
∞
,
0
)
(-\infty, 0)
(
−
∞
,
0
)
by choosing a number less than
0
0
0
, say
x
=
−
1
x = -1
x
=
−
1
.\(\newline\)
(
−
1
)
(
−
1
−
3
)
=
(
−
1
)
(
−
4
)
=
4
(-1)(-1 - 3) = (-1)(-4) = 4
(
−
1
)
(
−
1
−
3
)
=
(
−
1
)
(
−
4
)
=
4
, which is
≥
0
\geq 0
≥
0
.
Test Interval
0
,
3
0, 3
0
,
3
:
Test the interval
0
,
3
0, 3
0
,
3
by choosing a number between
0
0
0
and
3
3
3
, say
x
=
1
x = 1
x
=
1
.
(
1
)
(
1
−
3
)
=
(
1
)
(
−
2
)
=
−
2
(1)(1 - 3) = (1)(-2) = -2
(
1
)
(
1
−
3
)
=
(
1
)
(
−
2
)
=
−
2
, which is not
e
x
t
b
a
c
k
s
l
a
s
h
g
e
q
0
extbackslash geq 0
e
x
t
ba
c
k
s
l
a
s
h
g
e
q
0
.
Test Interval
3
,
∞
)
:
<
/
b
>
T
e
s
t
t
h
e
i
n
t
e
r
v
a
l
$
3
,
∞
)
b
y
c
h
o
o
s
i
n
g
a
n
u
m
b
e
r
g
r
e
a
t
e
r
t
h
a
n
$
3
3, \infty):</b> Test the interval \$3, \infty) by choosing a number greater than \$3
3
,
∞
)
:<
/
b
>
T
es
tt
h
e
in
t
er
v
a
l
$3
,
∞
)
b
yc
h
oos
in
g
an
u
mb
er
g
re
a
t
er
t
han
$3
, say
x
=
4
x = 4
x
=
4
.
(
4
)
(
4
−
3
)
=
(
4
)
(
1
)
=
4
(4)(4 - 3) = (4)(1) = 4
(
4
)
(
4
−
3
)
=
(
4
)
(
1
)
=
4
, which is
≥
0
\geq 0
≥
0
.
Combine Intervals:
Combine the intervals where the function is
≥
0
\geq 0
≥
0
.
x
x
x
is in
(
−
∞
,
0
]
(-\infty, 0]
(
−
∞
,
0
]
or
[
3
,
∞
)
[3, \infty)
[
3
,
∞
)
.
More problems from Solve quadratic inequalities
Question
Solve for
s
s
s
.
\newline
∣
s
∣
+
3
≥
8
|s| + 3 \geq 8
∣
s
∣
+
3
≥
8
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Posted 9 months ago
Question
Which compound inequality represents the value of
x
?
x ?
x
?
\newline
(
x
−
1
)
(
x
+
1
)
>
0
(x - 1)(x + 1) > 0
(
x
−
1
)
(
x
+
1
)
>
0
\newline
Get tutor help
Posted 9 months ago
Question
A particular company charges advertisers a one time cost of
$
500
\$500
$500
, in addition to
$
4.50
\$4.50
$4.50
for every one thousand times an advertisement is shown on the company's webpage. An advertiser wants its ad to appear
M
M
M
thousand times on the webpage, but does not want to spend more than
$
5
,
000
\$5,000
$5
,
000
. Which of the following inequalities best describes the situation?
\newline
Choices:
\newline
(A)
500
+
4.50
M
≥
5
,
000
500+4.50M\geq5,000
500
+
4.50
M
≥
5
,
000
\newline
(B)
4.50
+
500
M
>
5
,
000
4.50+500M>5,000
4.50
+
500
M
>
5
,
000
\newline
(C)
500
+
4.50
M
≤
5
,
000
500+4.50M\leq5,000
500
+
4.50
M
≤
5
,
000
\newline
(D)
500
+
4.50
M
<
5
,
000
500+4.50M<5,000
500
+
4.50
M
<
5
,
000
Get tutor help
Posted 1 year ago
Question
7
x
+
1
<
x
+
9
7x+1 < x+9
7
x
+
1
<
x
+
9
\newline
Which of the following best describes the solutions to the inequality shown?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
>
4
3
x > \frac{4}{3}
x
>
3
4
\newline
(B)
x
<
4
3
x < \frac{4}{3}
x
<
3
4
\newline
(C)
x
<
1
x < 1
x
<
1
\newline
(D)
x
<
5
3
x < \frac{5}{3}
x
<
3
5
Get tutor help
Posted 9 months ago
Question
52
−
3
x
<
−
14
52-3x < -14
52
−
3
x
<
−
14
\newline
Which of the following best describes the solutions to the inequality shown?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
>
−
38
3
x > -\frac{38}{3}
x
>
−
3
38
\newline
(B)
x
>
38
3
x > \frac{38}{3}
x
>
3
38
\newline
(C)
x
<
22
x < 22
x
<
22
\newline
(D)
x
>
22
x > 22
x
>
22
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Posted 1 year ago
Question
5
−
3
x
>
2
x
+
2
5-3x > 2x+2
5
−
3
x
>
2
x
+
2
\newline
Which of the following best describes the solutions to the inequality shown?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
<
7
5
x < \frac{7}{5}
x
<
5
7
\newline
(B)
x
<
3
x < 3
x
<
3
\newline
(C)
x
<
3
5
x < \frac{3}{5}
x
<
5
3
\newline
(D)
x
>
3
5
x > \frac{3}{5}
x
>
5
3
Get tutor help
Posted 1 year ago
Question
Rani is a real estate agent. For each house she sells, she pays
$
100
\$ 100
$100
in fees, but earns a commission of
1.8
%
1.8 \%
1.8%
of the selling price of the house. Rani's total profit from a particular house is
$
4
,
580
\$ 4,580
$4
,
580
. If
p
p
p
represents the selling price of the house, which equation best models the situation?
\newline
Choose
1
1
1
answer:
\newline
(A)
0.018
p
−
100
=
4580
0.018 p-100=4580
0.018
p
−
100
=
4580
\newline
(B)
0.018
p
+
100
=
4580
0.018 p+100=4580
0.018
p
+
100
=
4580
\newline
(C)
(
100
−
0.018
)
p
=
4580
(100-0.018) p=4580
(
100
−
0.018
)
p
=
4580
\newline
(D)
(
100
+
0.018
)
p
=
4580
(100+0.018) p=4580
(
100
+
0.018
)
p
=
4580
Get tutor help
Posted 1 year ago
Question
A commercial airplane that is
1
1
1
,
500
500
500
miles into a
2
2
2
,
500
500
500
-mile journey is traveling at
450
450
450
knots in still air when it picks up a tailwind of
150
150
150
knots (in the same direction). If
h
h
h
is the number of hours remaining in the airplane's flight, which of the following equations best describes the situation?
\newline
1
1
1
k
n
o
t
=
1.15
\mathrm{knot}=1.15
knot
=
1.15
miles per hour (mph)
\newline
Choose
1
1
1
answer:
\newline
(A)
1
,
500
+
690
h
=
2
,
500
1,500+690 h=2,500
1
,
500
+
690
h
=
2
,
500
\newline
(B)
1
,
500
+
600
h
=
2
,
500
1,500+600 h=2,500
1
,
500
+
600
h
=
2
,
500
\newline
(C)
1
,
500
−
600
h
=
2
,
500
1,500-600 h=2,500
1
,
500
−
600
h
=
2
,
500
\newline
(D)
1
,
500
−
690
h
=
2
,
500
1,500-690 h=2,500
1
,
500
−
690
h
=
2
,
500
Get tutor help
Posted 1 year ago
Question
A weeping willow that is
15
15
15
feet in height grows to a maximum height of
35
35
35
feet in
y
y
y
years at a constant rate of
24
24
24
inches per year. Which of the following equations best describes this situation?
\newline
1
1
1
foot
=
12
=12
=
12
inches
\newline
Choose
1
1
1
answer:
\newline
(A)
35
=
15
+
2
y
35=15+2 y
35
=
15
+
2
y
\newline
(B)
35
=
15
+
24
y
35=15+24 y
35
=
15
+
24
y
\newline
(C)
35
=
15
−
2
y
35=15-2 y
35
=
15
−
2
y
\newline
(D)
35
=
15
−
24
y
35=15-24 y
35
=
15
−
24
y
Get tutor help
Posted 1 year ago
Question
The gas mileage for a car is
23
23
23
miles per gallon when the car travels at
60
60
60
miles per hour. The car begins a trip with
13
13
13
gallons in its tank, travels at an average speed of
60
60
60
miles per hour for
h
h
h
hours, and ends the trip with
10
10
10
gallons in its tank. Which of the following equations best models this situation?
\newline
Choose
1
1
1
answer:
\newline
(A)
13
−
23
h
60
=
10
13-\frac{23 h}{60}=10
13
−
60
23
h
=
10
\newline
(B)
13
−
60
h
23
=
10
13-\frac{60 h}{23}=10
13
−
23
60
h
=
10
\newline
(C)
13
−
60
h
23
=
10
\frac{13-60 h}{23}=10
23
13
−
60
h
=
10
\newline
(D)
13
−
23
h
60
=
10
\frac{13-23 h}{60}=10
60
13
−
23
h
=
10
Get tutor help
Posted 1 year ago
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