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Math Problems
Grade 8
Negative Exponents
Subtract.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
1
x
−
4
−
5
x
+
6
=
\frac{1}{x-4}-\frac{5}{x+6}=
x
−
4
1
−
x
+
6
5
=
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Add.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
9
x
−
7
+
3
x
=
□
\frac{9}{x-7}+\frac{3}{x}=\square
x
−
7
9
+
x
3
=
□
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Add.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
1
7
x
2
−
7
x
+
6
7
x
2
+
14
x
=
\frac{1}{7 x^{2}-7 x}+\frac{6}{7 x^{2}+14 x}=
7
x
2
−
7
x
1
+
7
x
2
+
14
x
6
=
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Subtract.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
7
2
x
2
+
18
x
−
5
x
x
2
+
17
x
+
72
=
\frac{7}{2 x^{2}+18 x}-\frac{5 x}{x^{2}+17 x+72}=
2
x
2
+
18
x
7
−
x
2
+
17
x
+
72
5
x
=
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Evaluate the expression.
\newline
Do not round your answer.
\newline
(
4
+
3
)
2
+
5
=
(4+3)^{2}+5=
(
4
+
3
)
2
+
5
=
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Divide. Write the quotient in lowest terms.
\newline
12
÷
1
1
5
=
12 \div 1 \frac{1}{5}=
12
÷
1
5
1
=
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Divide. Write the quotient in lowest terms.
\newline
5
÷
3
1
3
=
5 \div 3 \frac{1}{3}=
5
÷
3
3
1
=
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Divide. Write the quotient in lowest terms.
\newline
8
÷
1
4
5
=
8 \div 1 \frac{4}{5}=
8
÷
1
5
4
=
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Rewrite the equation by completing the square.
\newline
x
2
+
7
x
+
12
=
0
(
x
+
□
)
2
=
□
\begin{array}{l} x^{2}+7 x+12=0 \\ (x+\square)^{2}=\square \end{array}
x
2
+
7
x
+
12
=
0
(
x
+
□
)
2
=
□
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7
x
+
10
y
=
60
7
x
−
2
y
=
240
\begin{aligned} 7 x+10 y & =60 \\ 7 x-2 y & =240 \end{aligned}
7
x
+
10
y
7
x
−
2
y
=
60
=
240
\newline
If
(
x
,
y
)
(x, y)
(
x
,
y
)
satisfies the given system of equations, what is the value of
x
x
x
?
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2
x
−
3
y
=
15
2 x-3 y=15
2
x
−
3
y
=
15
\newline
y
=
−
1
3
(
x
2
−
16
x
+
63
)
y=-\frac{1}{3}\left(x^{2}-16 x+63\right)
y
=
−
3
1
(
x
2
−
16
x
+
63
)
\newline
If
(
x
,
y
)
(x, y)
(
x
,
y
)
is a solution to the system of equations shown and
y
>
0
y>0
y
>
0
, what is the value of
x
x
x
?
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Distribute to create an equivalent expression with the fewest symbols possible.
\newline
(
6
m
−
7
)
⋅
4
=
(6 m-7) \cdot 4=
(
6
m
−
7
)
⋅
4
=
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Distribute to create an equivalent expression with the fewest symbols possible.
\newline
(
1
−
2
g
+
4
h
)
⋅
5
=
(1-2 g+4 h) \cdot 5=
(
1
−
2
g
+
4
h
)
⋅
5
=
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Distribute to create an equivalent expression with the fewest symbols possible.
\newline
6
(
5
x
−
3
)
=
6(5 x-3)=
6
(
5
x
−
3
)
=
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Distribute to create an equivalent expression with the fewest symbols possible.
\newline
4
(
x
−
2
+
y
)
=
4(x-2+y)=
4
(
x
−
2
+
y
)
=
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Distribute to create an equivalent expression with the fewest symbols possible.
\newline
1
2
(
2
a
−
6
b
+
8
)
=
\frac{1}{2}(2 a-6 b+8)=
2
1
(
2
a
−
6
b
+
8
)
=
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Distribute to create an equivalent expression with the fewest symbols possible.
\newline
(
6
e
−
3
f
−
4
)
⋅
2
=
(6 e-3 f-4) \cdot 2=
(
6
e
−
3
f
−
4
)
⋅
2
=
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Distribute to create an equivalent expression with the fewest symbols possible.
\newline
6
(
3
c
−
5
d
+
6
)
=
6(3 c-5 d+6)=
6
(
3
c
−
5
d
+
6
)
=
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Distribute to create an equivalent expression with the fewest symbols possible.
\newline
2
(
3
−
8
y
)
=
2(3-8 y)=
2
(
3
−
8
y
)
=
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Distribute to create an equivalent expression with the fewest symbols possible.
\newline
(
7
−
4
n
)
⋅
6
=
(7-4 n) \cdot 6=
(
7
−
4
n
)
⋅
6
=
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0.354
+
8.47
=
0.354+8.47=
0.354
+
8.47
=
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0.422
+
7.41
=
0.422+7.41=
0.422
+
7.41
=
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Evaluate.
\newline
21
−
1.026
=
21-1.026=
21
−
1.026
=
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The product
97
×
8
97 \times 8
97
×
8
equals
776
776
776
. Use the previous fact to evaluate as a decimal.
\newline
9.7
×
0.08
=
9.7 \times 0.08=
9.7
×
0.08
=
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