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 a systematic approach and justify each step.

1. **Distribute the left side**:
We start by applying the distributive property on the left side of the equation.
\[
2(x + 8) = 2 \cdot x + 2 \cdot 8
\]
This simplifies to:
\[
2x + 16
\]

So, the equation now looks like this:
\[
2x + 16 = 2x + 8
\]

2. **Subtract \(2x\) from both sides**:
To isolate the constants, we can subtract \(2x\) from both sides of the equation.
\[
(2x + 16) - 2x = (2x + 8) - 2x
\]
This simplifies to:
\[
16 = 8
\]

3. **Evaluate the resulting statement**:
The statement \(16 = 8\) is a contradiction since 16 does not equal 8. This means that the original equation has no solutions.

4. **Conclusion**:
Since we arrive at a false statement, we conclude that there are no values of \(x\) that satisfy the equation \( 2(x + 8) = 2x + 8\).

Thus, the final answer is that the equation has no solutions.