Answered

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Which property is not used to simplify the following expression?

[tex]\[
\begin{aligned}
2 \cdot(x+5)+7 x & =(2 x+10)+7 x \\
& =(10+2 x)+7 x \\
& =10+(2 x+7 x) \\
& =10+9 x \\
& =9 x+10
\end{aligned}
\][/tex]

A. commutative property of multiplication
B. distributive property
C. commutative property of addition
D. associative property of addition

Sagot :

GinnyAnswer
Let's go through the simplification step by step to identify which properties are used:

1. Distributive Property:
The expression [tex]\( 2 \cdot (x+5) + 7x \)[/tex] is simplified by distributing the 2 through the parentheses:
[tex]\[ 2 \cdot (x+5) + 7x = (2x + 10) + 7x \][/tex]
This step uses the distributive property.

2. Commutative Property of Addition:
Next, the expression [tex]\( (2x + 10) + 7x \)[/tex] is reordered to [tex]\( (10 + 2x) + 7x \)[/tex]:
[tex]\[ (2x + 10) + 7x = (10 + 2x) + 7x \][/tex]
This uses the commutative property of addition.

3. Associative Property of Addition:
Then, [tex]\( (10 + 2x) + 7x \)[/tex] is regrouped to [tex]\( 10 + (2x + 7x) \)[/tex]:
[tex]\[ (10 + 2x) + 7x = 10 + (2x + 7x) \][/tex]
This step uses the associative property of addition.

4. Simplifying within Parentheses:
Combine the like terms within the parentheses:
[tex]\[ 10 + (2x + 7x) = 10 + 9x \][/tex]

5. Commutative Property of Addition:
Finally, [tex]\( 10 + 9x \)[/tex] is reordered to [tex]\( 9x + 10 \)[/tex]:
[tex]\[ 10 + 9x = 9x + 10 \][/tex]
This again uses the commutative property of addition.

From the analysis, we can see that:
- The distributive property is used.
- The commutative property of addition is used.
- The associative property of addition is used.

However, the commutative property of multiplication is not used at any point during the simplification of this expression.
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