Ashleenbondidn
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]-6x - 42 = 2x - 22[/tex]
Step 3: [tex]-8x - 42 = -22[/tex]
Step 4: [tex]-8x = 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 :

GinnyAnsweridn
Let's analyze the steps Simon took to solve the equation and identify which property he used to get from step 3 to step 4.

Step 1:
[tex]\[ -6(x + 7) = 2(x - 11) \][/tex]

Step 2: Applied the distributive property to simplify both sides,
[tex]\[ -6x - 42 = 2x - 22 \][/tex]

Step 3: Combined like terms,
[tex]\[ -8x - 42 = -22 \][/tex]

Step 4: Isolated the term involving [tex]\(x\)[/tex],
[tex]\[ -8x = 20 \][/tex]

To move from step 3 to step 4, Simon needed to isolate the term [tex]\(-8x\)[/tex] on the left side of the equation. This was done by adding 42 to both sides of the equation.

Here's how the transition looks with that operation explicitly shown:

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

Adding 42 to both sides,
[tex]\[ -8x - 42 + 42 = -22 + 42 \][/tex]

Simplifying,
[tex]\[ -8x = 20 \][/tex]

The property used in this step is the addition property of equality, which states that if the same value is added to both sides of an equation, the equality is still maintained.

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