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Math Problems
Grade 8
Solve multi-step equations with fractional coefficients
Solve for all values of
x
x
x
:
\newline
(
7
x
−
10
)
2
+
(
7
x
−
10
)
=
0
(7 x-10)^{2}+(7 x-10)=0
(
7
x
−
10
)
2
+
(
7
x
−
10
)
=
0
\newline
Answer:
x
=
x=
x
=
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−
5
b
+
2
(
b
−
1
)
≥
6
−
(
2
b
−
1
)
+
2
b
-5 b+2(b-1) \geq 6-(2 b-1)+2 b
−
5
b
+
2
(
b
−
1
)
≥
6
−
(
2
b
−
1
)
+
2
b
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Solve for p.
\newline
2
3
p
=
8
9
\frac{2}{3}p = \frac{8}{9}
3
2
p
=
9
8
\newline
p
=
□
p=\square
p
=
□
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Solve
x
2
−
4
=
x
3
+
2
\frac{x}{2}-4=\frac{x}{3}+2
2
x
−
4
=
3
x
+
2
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Solve for
x
\mathrm{x}
x
.
\newline
x
+
3
8
=
x
−
6
5
\frac{x+3}{8}=\frac{x-6}{5}
8
x
+
3
=
5
x
−
6
\newline
Answer:
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Solve for
x
\mathrm{x}
x
.
\newline
5
x
−
1
8
=
5
x
+
7
9
\frac{5 x-1}{8}=\frac{5 x+7}{9}
8
5
x
−
1
=
9
5
x
+
7
\newline
Answer:
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Solve for
x
\mathrm{x}
x
.
\newline
x
+
9
2
=
4
x
−
3
9
\frac{x+9}{2}=\frac{4 x-3}{9}
2
x
+
9
=
9
4
x
−
3
\newline
Answer:
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Solve for
x
\mathrm{x}
x
.
\newline
4
x
+
9
x
−
2
=
3
5
\frac{4 x+9}{x-2}=\frac{3}{5}
x
−
2
4
x
+
9
=
5
3
\newline
Answer:
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Solve for
x
\mathrm{x}
x
.
\newline
−
7
+
9
2
=
2
x
−
7
6
-7+\frac{9}{2}=\frac{2 x-7}{6}
−
7
+
2
9
=
6
2
x
−
7
\newline
Answer:
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Solve for
x
\mathrm{x}
x
.
\newline
−
1
+
5
4
=
2
x
−
5
12
-1+\frac{5}{4}=\frac{2 x-5}{12}
−
1
+
4
5
=
12
2
x
−
5
\newline
Answer:
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Solve for
x
\mathrm{x}
x
.
\newline
2
−
1
4
=
2
x
−
5
12
2-\frac{1}{4}=\frac{2 x-5}{12}
2
−
4
1
=
12
2
x
−
5
\newline
Answer:
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In
△
D
E
F
,
m
∠
D
=
(
10
x
−
13
)
∘
,
m
∠
E
=
(
x
−
4
)
∘
\triangle \mathrm{DEF}, \mathrm{m} \angle D=(10 x-13)^{\circ}, \mathrm{m} \angle E=(x-4)^{\circ}
△
DEF
,
m
∠
D
=
(
10
x
−
13
)
∘
,
m
∠
E
=
(
x
−
4
)
∘
, and
m
∠
F
=
(
2
x
+
15
)
∘
\mathrm{m} \angle F=(2 x+15)^{\circ}
m
∠
F
=
(
2
x
+
15
)
∘
. Find
m
∠
E
\mathrm{m} \angle E
m
∠
E
.
\newline
Answer:
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In
△
B
C
D
,
m
∠
B
=
(
8
x
+
12
)
∘
,
m
∠
C
=
(
3
x
−
17
)
∘
\triangle \mathrm{BCD}, \mathrm{m} \angle B=(8 x+12)^{\circ}, \mathrm{m} \angle C=(3 x-17)^{\circ}
△
BCD
,
m
∠
B
=
(
8
x
+
12
)
∘
,
m
∠
C
=
(
3
x
−
17
)
∘
, and
m
∠
D
=
(
x
+
17
)
∘
\mathrm{m} \angle D=(x+17)^{\circ}
m
∠
D
=
(
x
+
17
)
∘
. Find
m
∠
D
\mathrm{m} \angle D
m
∠
D
.
\newline
Answer:
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In
△
H
I
J
,
m
∠
H
=
(
6
x
+
10
)
∘
,
m
∠
I
=
(
3
x
−
6
)
∘
\triangle \mathrm{HIJ}, \mathrm{m} \angle H=(6 x+10)^{\circ}, \mathrm{m} \angle I=(3 x-6)^{\circ}
△
HIJ
,
m
∠
H
=
(
6
x
+
10
)
∘
,
m
∠
I
=
(
3
x
−
6
)
∘
, and
m
∠
J
=
(
6
x
+
11
)
∘
\mathrm{m} \angle J=(6 x+11)^{\circ}
m
∠
J
=
(
6
x
+
11
)
∘
.
\newline
Find
m
∠
J
\mathrm{m} \angle J
m
∠
J
.
\newline
Answer:
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Solve for
w
\mathrm{w}
w
.
\newline
−
1
=
w
7
-1=\frac{w}{7}
−
1
=
7
w
\newline
Answer:
w
=
w=
w
=
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Solve for
a
a
a
.
\newline
a
0.5
+
2.4
=
−
2.6
\frac{a}{0.5}+2.4=-2.6
0.5
a
+
2.4
=
−
2.6
\newline
Answer:
a
=
a=
a
=
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Rewrite in simplest terms:
−
2
(
4
x
+
1
)
+
6
(
5
x
−
1
)
-2(4 x+1)+6(5 x-1)
−
2
(
4
x
+
1
)
+
6
(
5
x
−
1
)
\newline
Answer:
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Find `x` value from the equation
\newline
3
(
7
−
2
x
)
=
5
(
4
x
+
11
)
3^{(7-2x)}=5^{(4x+11)}
3
(
7
−
2
x
)
=
5
(
4
x
+
11
)
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Evaluate
−
y
+
(
−
z
)
+
7.99
-y+(-z)+7.99
−
y
+
(
−
z
)
+
7.99
where
y
=
1.46
y=1.46
y
=
1.46
and
z
=
3.82
z=3.82
z
=
3.82
.
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Solve for
d
d
d
.
\newline
3
2
=
5
d
−
1
2
\frac{3}{2}=5 d-\frac{1}{2}
2
3
=
5
d
−
2
1
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Solve for
q
q
q
.
\newline
3
(
q
+
4
3
)
=
2
3\left(q+\frac{4}{3}\right)=2
3
(
q
+
3
4
)
=
2
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Solve for
r
r
r
.
\newline
4
r
−
6
r
−
7
=
2
\frac{4 r-6}{r-7}=2
r
−
7
4
r
−
6
=
2
\newline
r
=
r=
r
=
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Solve for
k
k
k
.
\newline
6
2
k
−
6
=
3
k
=
\begin{array}{l} \frac{6}{2 k-6}=3 \\ k= \end{array}
2
k
−
6
6
=
3
k
=
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What is the amplitude of
\newline
g
(
x
)
=
8
cos
(
5
π
x
+
3
π
2
)
−
9
?
g(x)=8 \cos \left(5 \pi x+\frac{3 \pi}{2}\right)-9 ?
g
(
x
)
=
8
cos
(
5
π
x
+
2
3
π
)
−
9
?
\newline
units
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What is the amplitude of
y
=
2
cos
(
7
x
+
5
)
+
1
y=2 \cos (7 x+5)+1
y
=
2
cos
(
7
x
+
5
)
+
1
?
\newline
units
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If
\newline
(
20
y
+
5
)
(
4
y
−
30
)
=
80
y
2
+
b
y
(20 y+5)(4 y-30)=80 y^{2}+b y
(
20
y
+
5
)
(
4
y
−
30
)
=
80
y
2
+
b
y
\newline
for all values of
y
y
y
where
b
b
b
is a constant, then which of the following is the value of
b
b
b
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
580
-580
−
580
\newline
(B)
−
40
-40
−
40
\newline
(C)
0
0
0
\newline
(D)
620
620
620
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If
f
(
x
)
=
(
2
x
−
1
)
(
x
−
6
)
(
3
x
+
1
)
f(x)=(2 x-1)(x-6)(3 x+1)
f
(
x
)
=
(
2
x
−
1
)
(
x
−
6
)
(
3
x
+
1
)
, what is the value of
f
(
1
2
)
f\left(\frac{1}{2}\right)
f
(
2
1
)
?
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If
−
24
=
3
(
1
+
r
)
-24=3(1+r)
−
24
=
3
(
1
+
r
)
, what is the value of
7
(
1
+
r
)
7(1+r)
7
(
1
+
r
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
56
-56
−
56
\newline
(B)
−
24
-24
−
24
\newline
(C)
−
9
-9
−
9
\newline
(D)
−
8
-8
−
8
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1
4
v
=
2
+
3
\frac{1}{4} v=2+3
4
1
v
=
2
+
3
\newline
Given the equation, what is the value of
\newline
6
v
−
17
+
18
−
19
+
20
?
6 v-17+18-19+20 ?
6
v
−
17
+
18
−
19
+
20
?
\newline
Choose
1
1
1
answer:
\newline
(A)
14
14
14
\newline
(B)
32
32
32
\newline
(C)
122
122
122
\newline
(D)
144
144
144
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Factor
72
y
+
108
z
72 y+108 z
72
y
+
108
z
to identify the equivalent expressions.
\newline
Choose
2
2
2
answers:
\newline
A
9
(
7
y
+
12
z
)
9(7 y+12 z)
9
(
7
y
+
12
z
)
\newline
B
36
(
2
y
+
3
z
)
36(2 y+3 z)
36
(
2
y
+
3
z
)
\newline
c
6
(
18
y
+
12
z
)
6(18 y+12 z)
6
(
18
y
+
12
z
)
\newline
D
12
(
6
y
+
9
z
)
12(6 y+9 z)
12
(
6
y
+
9
z
)
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What is the slope of the line?
\newline
−
4
x
+
7
=
2
y
−
3
-4x+7=2y-3
−
4
x
+
7
=
2
y
−
3
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
2
-\frac{1}{2}
−
2
1
\newline
(B)
−
1
3
-\frac{1}{3}
−
3
1
\newline
(C)
−
3
-3
−
3
\newline
(D)
−
2
-2
−
2
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What is the slope of the line?
\newline
3
(
y
−
1
)
=
2
x
+
2
3(y-1)=2x+2
3
(
y
−
1
)
=
2
x
+
2
\newline
Choose
1
1
1
answer:
\newline
(A)
2
3
\frac{2}{3}
3
2
\newline
(B)
1
3
\frac{1}{3}
3
1
\newline
(C)
5
3
\frac{5}{3}
3
5
\newline
(D)
4
3
\frac{4}{3}
3
4
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If
−
8
−
8
y
=
6
−
2
y
-8-8y=6-2y
−
8
−
8
y
=
6
−
2
y
, what is the value of
y
y
y
?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
−
3
7
y=-\frac{3}{7}
y
=
−
7
3
\newline
(B)
y
=
3
7
y=\frac{3}{7}
y
=
7
3
\newline
(C)
y
=
7
3
y=\frac{7}{3}
y
=
3
7
\newline
(D)
y
=
−
7
3
y=-\frac{7}{3}
y
=
−
3
7
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What is the slope of the line?
\newline
−
4
x
+
7
=
2
y
−
3
-4x+7=2y-3
−
4
x
+
7
=
2
y
−
3
\newline
Choose
1
1
1
answer:
\newline
(A)
−
2
-2
−
2
\newline
(B)
−
1
3
-\frac{1}{3}
−
3
1
\newline
(C)
−
3
-3
−
3
\newline
(D)
−
1
2
-\frac{1}{2}
−
2
1
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Solve for x.
\newline
(
2
7
)
x
=
−
14
(\frac{2}{7})x= -14
(
7
2
)
x
=
−
14
\newline
x
=
x =
x
=
______
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