Solve the equation using the steps: 2(x + 8) = 2x + 8

Question

Step 1: Use the __________ Property to get ________ resulting equation.

Step 2: Use the ________ Property to get ___________ resulting equation.

Step 3: There is/are _________ solution(s).

Answer 1

Let's solve the equation \( 2(x + 8) = 2x + 8 \) step by step.

Step 1: Use the Distributive Property to get 2x + 16 resulting equation.

Starting with the original equation: \[ 2(x + 8) = 2x + 8 \]

Applying the Distributive Property: \[ 2x + 16 = 2x + 8 \]

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Step 2: Use the Subtraction Property of Equality to get 16 = 8 resulting equation.

Subtract \( 2x \) from both sides: \[ 2x + 16 - 2x = 2x + 8 - 2x \] This simplifies to: \[ 16 = 8 \]

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Step 3: There is/are no solutions.

The statement \( 16 = 8 \) is false, indicating that there are no values of \( x \) that satisfy the original equation.

Final summary:

1. Step 1: Use the Distributive Property to get 2x + 16 resulting equation.
2. Step 2: Use the Subtraction Property of Equality to get 16 = 8 resulting equation.
3. Step 3: There is/are no solutions.