AnswersAG Q1 Keystone Algebra 1 Block 26-27 DDiamondExpanding Expressions

Expanding Expressions Answers

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1
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Which can be used to expand the expression below?

Question illustration
A
associative property
B
commutative property
C
distributive property
D
subtracting
2
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Check all that you included in your response.

A
The expansion is not correct.
B
The –6 did not get distributed properly.
C
The second term should be positive.
3

Which expression is equivalent to –2(5x – 0.75)?

A
10x – 0.75
B
10x + 0.75
C
–10x – 1.5
D
–10x + 1.5
4

Which expression is equivalent to ?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
5

Question text not available

Answer:

Answer

6

Which expressions are equivalent to ? Check all that apply.

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
–6x + 1
E
–6x + 9
F
–6x – 9
7

Are the expressions –0.5(3x + 5) and –1.5x + 2.5 equivalent? Explain why or why not.

Answer:

Using the distributive property to expand the first expression, you would get -1.5x - 2.5. Since the constant term does not have the same sign as the second expression, the two expressions are not equivalent. Also, if you substitute in a value for x and evaluate each expression, the values will not be equal.

8

What is –9.2(8x – 4) + 0.7(2 + 6.3x) simplified?

A
–69.19x – 32.39
B
–69.19x + 38.2
C
–72.2x + 41.21
D
75x – 338.2
9

Which expressions are equivalent to ? Check all that apply.

Question illustration
A
-1
B
29
C
2 (three-fourths x + 7) + (negative 3) left-bracket one-half x + (negative 5) right-bracket
Option C
D
2 (three-fourths x) + 2 (7) + 3 (one-half x) + 3 (negative 5)
Option D
E
2 (three-fourths x) + 2 (7) + (negative 3) (one-half x) + (negative 3) (negative 5)
Option E
10

✔ 68910.5

A
6
B
8
C
9
D
10.5
11

Compare and contrast expanding and simplifying algebraic expressions with simplifying numeric expressions. For example, compare simplifying 3(x – 2) + (x – 1) with 3(5 – 2) + (5 – 1).

Answer:

With algebraic expressions, you can’t add and subtract any terms like you can add and subtract numbers. Terms must be like terms in order to combine them. So, you can’t always simplify an algebraic expression by following the order of operations. You have to use the distributive property to rewrite the expression and then combine like terms to simplify. With numeric expressions, you can either simplify inside the parentheses first or use the distributive property first.

12

Check all that you included in your response.

A
Use the distributive property to expand the first expression.
B
While the first terms are the same, the constant is positive in one expression and negative in the other.
C
If you evaluate the expressions for a value of x, they are not equal.
13

6✔ 81214

A
6
B
8
C
12
D
14
14

Sample response: With algebraic expressions, you can’t add and subtract any terms like you can add and subtract numbers. Terms must be like terms in order to combine them. So, you can’t always simplify an algebraic expression by following the order of operations. You have to use the distributive property to rewrite the expression and then combine like terms to simplify. With numeric expressions, you can either simplify inside the parentheses first or use the distributive property first. Check al

A
Algebraic expressions have terms.
B
Terms must be like to add and subtract.
C
You can’t always follow the order of operations with algebraic expressions.

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