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Solve the equation justifying each step with the correct reasoning.

2(x+8)=2x+8 (5 points)
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Step 1: Response area Property to get Response area simplified equation

Step 2: Response area Property to get Response area simplified equation

For this equation, there is/are

1 answer

Let's solve the equation step-by-step and justify each step with the correct reasoning.

Step 1: Expand the left side.

Response area: Distributive property
Response area: 2x + 16

Justification: We apply the distributive property, which states that \( a(b+c) = ab + ac \). Here, \( 2(x + 8) \) becomes \( 2x + 16 \).

So, we rewrite the equation as: \[ 2x + 16 = 2x + 8 \]

Step 2: Subtract \( 2x \) from both sides.

Response area: Subtraction property of equality
Response area: 16 = 8

Justification: By subtracting \( 2x \) from both sides, we maintain the equality according to the subtraction property of equality, which states that if \( a = b \), then \( a - c = b - c \).

Thus, we can now see: \[ 16 = 8 \]

For this equation, there is/are no solution because \( 16 \) does not equal \( 8 \).