AnswersPre-Algebra A-CRExpressions with and without Parentheses

Equivalent Expressions Answers

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Randy is checking to determine if the expressions and are equivalent. When , he correctly finds that both expressions have a value of 20. When , he correctly evaluates the first expression to find that .What is the value of the second expression when , and are the two expressions equivalent?

Question illustration
A
The value of the second expression is 7, so the expressions are not equivalent.
B
The value of the second expression is 12, so the expressions are not equivalent.
C
The value of the second expression is 14, so the expressions are equivalent.
D
The value of the second expression is 20, so the expressions are equivalent.
2
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After substituting, what is the first operation performed when evaluating for ?

Question illustration
A
addition
B
multiplication
C
subtraction
D
division
3

Maria determined that these expressions are equivalent expressions using the values of and . Which statements are true? Check all that apply. and

Question illustration
A
The expressions are only equivalent when evaluated with odd values.
B
The expressions are only equivalent for and .
Option B
C
The expressions should have been evaluated with one odd value and one even value.
D
The expressions have equivalent values when .
Option D
E
When , the first expression has a value of 3 and the second expression has a value of 4.
Option E
F
The expressions have equivalent values for any value of x.
G
When , both expressions have a value of 33.
Option G
4

Which expression is equivalent to ?

Question illustration
A
n m + n
Option A
B
z + m z
Option B
C
m z + n
Option C
D
z + n m
Option D
5

Which expressions are equivalent to ? Check all that apply.

Question illustration
A
1 + 3 + 8 d + 5 + 7
Option A
B
8 d + one-third + StartFraction 5 Over 7 EndFraction
Option B
C
StartFraction 1 Over 7 EndFraction + 8 d + StartFraction 5 Over 3 EndFraction
Option C
D
One-third + StartFraction 5 Over 7 EndFraction + 8 d
Option D
E
3 + 8 d + 7
Option E
F
8 d + one-third + StartFraction 7 Over 5 EndFraction
Option F
G
StartFraction 5 Over 7 EndFraction + one-third + 8 d
Option G
6

A math class is having a discussion on how to determine if the expressions and are equivalent. The class has suggested four different methods.Which describes the correct method?

Question illustration
A
Both expressions should be evaluated by substituting one value for x. If the final values of the expressions are both positive after the substitution, then the two expressions must be equivalent.
B
Both expressions should be evaluated by substituting with one value for x. If the final values of the expressions are the same, then the two expressions must be equivalent.
C
Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are positive, then the two expressions must be equivalent.
D
Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.
7

Which best proves why the expressions and must be equivalent expressions?

Question illustration
A
When , both expressions have a value of 30.
Option A
B
When , both expressions have a value of 42.
Option B
C
When , both expressions have a value of 18, and when , both expressions have a value of 60.
Option C
D
When , both expressions have a value of 15, and when , both expressions have a value of 39.
Option D
8

Which expression is equivalent to ?

Question illustration
A
7 a c
Option A
B
a minus (c + 7)
Option B
C
(c + 7) minus a
Option C
D
(a + c) + 7
Option D
9

Which property was applied to create this equivalent expression?

Question illustration
A
the commutative property only
B
the associative property only
C
the distributive property only
D
both the commutative property and the associative property
10

Vance used the associative property to find the equivalent expression of . His work is shown below. Did Vance apply the associative property correctly? Why or why not?

Question illustration
A
Yes, the terms with variables should be written first.
B
Yes, the terms can be regrouped and still be equivalent.
C
No, the order of the terms should have been changed.
D
No, the addition symbol was dropped in the second expression.

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