Solve the equation justifying each step with the correct reasoning.

Question

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.