Question

Solve the equation justifying each step with the correct reasoning.
2(x+8)=2x+8

Answer 1

To solve the equation \( 2(x+8) = 2x + 8 \), we will follow these steps:

1. **Distribute on the left side**:
\[
2(x+8) = 2 \cdot x + 2 \cdot 8
\]
This simplifies to:
\[
2x + 16
\]
So the equation now reads:
\[
2x + 16 = 2x + 8
\]

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

3. **Analyze the resulting statement**:
The statement \(16 = 8\) is a contradiction. This means that there is no value of \(x\) that can satisfy the original equation.

Thus, we conclude that the equation has **no solution**.