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Math Problems
Algebra 1
Properties of equality
Which property of equality is shown below?
\newline
If:
−
91
=
h
−
(
−
79
)
-91 = h - (-79)
−
91
=
h
−
(
−
79
)
\newline
Then:
−
7
⋅
−
91
=
−
7
(
h
−
(
−
79
)
)
-7 \cdot -91 = -7(h - (-79))
−
7
⋅
−
91
=
−
7
(
h
−
(
−
79
))
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Which property of equality is shown below?
\newline
If:
60
x
=
−
62
60x = -62
60
x
=
−
62
\newline
Then:
60
x
−
90
=
−
62
−
90
60x - 90 = -62 - 90
60
x
−
90
=
−
62
−
90
\newline
Choices:
\newline
(A) Addition Property of Equality
\newline
(B) Subtraction Property of Equality
\newline
(C) Multiplication Property of Equality
\newline
(D) Division Property of Equality
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Which property of equality is shown below?
\newline
If:
84
=
q
−
r
84 = q - r
84
=
q
−
r
\newline
Then:
84
⋅
−
34
=
(
q
−
r
)
⋅
−
34
84 \cdot -34 = (q - r) \cdot -34
84
⋅
−
34
=
(
q
−
r
)
⋅
−
34
\newline
Choices:
\newline
(A) Addition Property of Equality
\newline
(B) Subtraction Property of Equality
\newline
(C) Multiplication Property of Equality
\newline
(D) Division Property of Equality
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Which property of equality is shown below?
\newline
If:
x
=
8
+
w
x = 8 + w
x
=
8
+
w
\newline
Then:
x
+
y
=
8
+
w
+
y
x + y = 8 + w + y
x
+
y
=
8
+
w
+
y
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Which property of equality is shown below?
\newline
If:
−
27
=
89
+
c
-27 = 89 + c
−
27
=
89
+
c
\newline
Then:
−
27
52
=
89
+
c
52
-\frac{27}{52} = \frac{89 + c}{52}
−
52
27
=
52
89
+
c
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Which property of equality is shown below?
\newline
If:
19
+
c
=
d
19 + c = d
19
+
c
=
d
\newline
Then:
(
19
+
c
)
⋅
37
=
d
⋅
37
(19 + c) \cdot 37 = d \cdot 37
(
19
+
c
)
⋅
37
=
d
⋅
37
\newline
Choices:
\newline
(A) Addition Property of Equality
\newline
(B) Subtraction Property of Equality
\newline
(C) Multiplication Property of Equality
\newline
(D) Division Property of Equality
Get tutor help
Which property of equality is shown below?
\newline
If:
c
=
b
+
(
−
86
)
c = b + (-86)
c
=
b
+
(
−
86
)
\newline
Then:
c
d
=
b
+
(
−
86
)
d
\frac{c}{d} = \frac{b + (-86)}{d}
d
c
=
d
b
+
(
−
86
)
\newline
Choices:
\newline
(A) Addition Property of Equality
\newline
(B) Subtraction Property of Equality
\newline
(C) Multiplication Property of Equality
\newline
(D) Division Property of Equality
Get tutor help
When solving an equation, Francesca's first step is shown below. Which property justifies Francesca's first step?
\newline
Original Equation:
\newline
5
x
+
3
=
−
4
5 x+3=-4
5
x
+
3
=
−
4
\newline
First Step:
\newline
5
x
=
−
7
5 x=-7
5
x
=
−
7
\newline
division property of equality
\newline
subtraction property of equality
\newline
commutative property of addition
\newline
associative property of multiplication
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When solving an equation, Carmen's first step is shown below. Which property justifies Carmen's first step?
\newline
Original Equation:
\newline
4
x
⋅
−
2
=
2
4 x \cdot-2=2
4
x
⋅
−
2
=
2
\newline
First Step:
\newline
4
⋅
−
2
x
=
2
4 \cdot-2 x=2
4
⋅
−
2
x
=
2
\newline
multiplication property of equality
\newline
division property of equality
\newline
commutative property of multiplication
\newline
distributive property of multiplication over addition
Get tutor help
When solving an equation, Francesca's first step is shown below. Which property justifies Francesca's first step?
\newline
Original Equation:
\newline
4
x
⋅
−
2
=
2
4 x \cdot-2=2
4
x
⋅
−
2
=
2
\newline
First Step:
\newline
4
⋅
−
2
x
=
2
4 \cdot-2 x=2
4
⋅
−
2
x
=
2
\newline
division property of equality
\newline
commutative property of multiplication
\newline
associative property of multiplication
\newline
addition property of equality
Get tutor help
When solving an equation, Emily's first step is shown below. Which property justifies Emily's first step?
\newline
Original Equation:
\newline
5
x
+
5
=
−
5
5 x+5=-5
5
x
+
5
=
−
5
\newline
First Step:
\newline
5
x
=
−
10
5 x=-10
5
x
=
−
10
\newline
commutative property of addition
\newline
subtraction property of equality
\newline
associative property of multiplication
\newline
multiplication property of equality
Get tutor help
When solving an equation, Emily's first step is shown below. Which property justifies Emily's first step?
\newline
Original Equation:
\newline
−
3
x
+
x
2
−
3
=
0
-3 x+x^{2}-3=0
−
3
x
+
x
2
−
3
=
0
\newline
First Step:
\newline
x
2
−
3
x
−
3
=
0
x^{2}-3 x-3=0
x
2
−
3
x
−
3
=
0
\newline
associative property of multiplication
\newline
commutative property of multiplication
\newline
commutative property of addition
\newline
addition property of equality
Get tutor help
When solving an equation, Emily's first step is shown below. Which property justifies Emily's first step?
\newline
Original Equation:
\newline
3
(
−
5
x
)
=
5
3(-5 x)=5
3
(
−
5
x
)
=
5
\newline
First Step:
\newline
(
3
⋅
−
5
)
x
=
5
(3 \cdot-5) x=5
(
3
⋅
−
5
)
x
=
5
\newline
subtraction property of equality
\newline
associative property of multiplication
\newline
multiplication property of equality
\newline
commutative property of multiplication
Get tutor help
When solving an equation, Bianca's first step is shown below. Which property justifies Bianca's first step?
\newline
Original Equation:
\newline
−
4
x
=
8
-4 x=8
−
4
x
=
8
\newline
First Step:
\newline
x
=
−
2
x=-2
x
=
−
2
\newline
addition property of equality
\newline
distributive property of multiplication over addition
\newline
commutative property of addition
\newline
division property of equality
Get tutor help
When solving an equation, Bianca's first step is shown below. Which property justifies Bianca's first step?
\newline
Original Equation:
\newline
−
2
x
=
−
8
-2 x=-8
−
2
x
=
−
8
\newline
First Step:
\newline
x
=
4
x=4
x
=
4
\newline
division property of equality
\newline
subtraction property of equality
\newline
associative property of addition
\newline
commutative property of addition
Get tutor help
When solving an equation, Drew's first step is shown below. Which property justifies Drew's first step?
\newline
Original Equation:
\newline
1
3
x
=
−
4
\frac{1}{3} x=-4
3
1
x
=
−
4
\newline
First Step:
\newline
x
=
−
12
x=-12
x
=
−
12
\newline
associative property of addition
\newline
multiplication property of equality
\newline
subtraction property of equality
\newline
commutative property of multiplication
Get tutor help
When solving an equation, Drew's first step is shown below. Which property justifies Drew's first step?
\newline
Original Equation:
\newline
5
+
(
4
+
x
)
=
2
5+(4+x)=2
5
+
(
4
+
x
)
=
2
\newline
First Step:
\newline
(
5
+
4
)
+
x
=
2
(5+4)+x=2
(
5
+
4
)
+
x
=
2
\newline
associative property of addition
\newline
commutative property of addition
\newline
addition property of equality
\newline
multiplication property of equality
Get tutor help
When solving an equation, Carmen's first step is shown below. Which property justifies Carmen's first step?
\newline
Original Equation:
\newline
5
+
(
2
+
x
)
=
4
5+(2+x)=4
5
+
(
2
+
x
)
=
4
\newline
First Step:
\newline
(
5
+
2
)
+
x
=
4
(5+2)+x=4
(
5
+
2
)
+
x
=
4
\newline
division property of equality
\newline
subtraction property of equality
\newline
distributive property of multiplication over addition
\newline
associative property of addition
Get tutor help
When solving an equation, Anne's first step is shown below. Which property justifies Anne's first step?
\newline
Original Equation:
\newline
−
1
2
x
=
4
-\frac{1}{2} x=4
−
2
1
x
=
4
\newline
First Step:
\newline
x
=
−
8
x=-8
x
=
−
8
\newline
multiplication property of equality
\newline
addition property of equality
\newline
associative property of addition
\newline
commutative property of addition
Get tutor help
When solving an equation, Carmen's first step is shown below. Which property justifies Carmen's first step?
\newline
Original Equation:
\newline
5
+
(
2
+
x
)
=
5
5+(2+x)=5
5
+
(
2
+
x
)
=
5
\newline
First Step:
\newline
(
5
+
2
)
+
x
=
5
(5+2)+x=5
(
5
+
2
)
+
x
=
5
\newline
associative property of multiplication
\newline
associative property of addition
\newline
commutative property of addition
\newline
multiplication property of equality
Get tutor help
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