Answered

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Select the correct answer.

Simon used these steps to solve an equation:

Step 1: [tex]\(-6(x+7)=2(x-11)\)[/tex]
Step 2: [tex]\(-6 x-42=2 x-22\)[/tex]
Step 3: [tex]\(-8 x-42=-22\)[/tex]
Step 4: [tex]\(-8 x=20\)[/tex]

Which property did he use to get from Step 3 to Step 4?

A. Addition property of equality
B. Distributive property
C. Subtraction property of equality
D. Transitive property

Sagot :

GinnyAnswer
To determine which property Simon used to get from Step 3 to Step 4, let's carefully examine the transformation between these steps.

Starting from Step 3:
[tex]\[ -8x - 42 = -22 \][/tex]

To isolate the [tex]\( x \)[/tex] term, we need to eliminate the constant term (i.e., [tex]\(-42\)[/tex]). We do this by adding 42 to both sides of the equation:

[tex]\[ -8x - 42 + 42 = -22 + 42 \][/tex]

Simplifying both sides, we get:
[tex]\[ -8x = 20 \][/tex]

So, to get from Step 3 to Step 4, Simon added 42 to both sides of the equation. This operation follows the addition property of equality, which states that you can add the same number to both sides of an equation without changing the equality.

Thus, the correct answer is:
A. addition property of equality
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