olve the equation justifying each step with the correct reasoning.

Question

2(x+8)=2x+8
(5 points)
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Step 1: ______________Property to get
Step 2: _______________simplified equation

For this equation, there is/are Response area

Properties and Reasons
Equation simplified

Answer 1

Let's solve the equation step by step, providing justifications for each action. The equation to solve is:

\[ 2(x+8) = 2x + 8 \]

Step 1: Distribute the left side using the Distributive Property.

\[ 2(x+8) = 2 \cdot x + 2 \cdot 8 \rightarrow 2x + 16 \]

This gives us:

\[ 2x + 16 = 2x + 8 \]

Step 2: Simplify the equation to isolate the terms on one side. Subtract \( 2x \) from both sides.

\[ 2x + 16 - 2x = 2x + 8 - 2x \rightarrow 16 = 8 \]

Now we have a contradiction (16 = 8), indicating that there is no solution.

Summary:

• Step 1: Distributive Property to get \( 2x + 16 = 2x + 8 \)
• Step 2: Simplified equation to \( 16 = 8 \)

For this equation, there is/are: no solution.