Question

Select the correct answer.
The given equation has been solved in the table.

Answer 1

Answer:

D.  The subtraction property of equality was not applied to solve this equation.

Step-by-step explanation:

Step 1:  Given

$\sf \dfrac{x}{2}-7=-7$

Step 2:  Addition Property of Equality

(add 7 to both sides)

$\implies \sf \dfrac{x}{2}-7+7=-7+7$

Step 3:  Simplify

$\implies \sf \dfrac{x}{2}=0$

Step 4:  Multiplication Property of Equality

(multiply both sides by 2)

$\implies \sf 2 \cdot \dfrac{x}{2}=2 \cdot0$

Step 5:  Simplify

$\implies \sf x=0$

Answer 2

Answer:

D) The subtraction property of equality was not applied to solve this equation.

Step-by-step explanation:

Properties of Equality:

Addition: If a = b, then a + c = b + c

Subtraction: If a = b, then a - c = b - c

Multiplication: If a = b, then ac = bc

Division: If a = b, then a ÷ c = b ÷ c

1. Given:

$\sf \implies \dfrac{x}{2}-7=-7$

2. Addition Property of Equality:

$\sf \dfrac{x}{2}-7=-7\ \textsf{[add 7 to both sides]}\\\\\implies\dfrac{x}{2}-7+7=-7+7$

3. Simplify:

$\sf \dfrac{x}{2}-7+7=-7+7\\\\\implies \dfrac{x}{2}=0$

4. Multiplication Property of Equality:

$\sf 2\left(\dfrac{x}{2}\right)=0(2)\\\\\implies \dfrac{2x}{2}=0$

5. Simplify:

$\sf \implies x=0$

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