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

Answer 1

We will solve the equation $2(x+8)=2x+8$ step by step, justifying each step.

1. Distribute on the left side: $$2(x+8)=2x+16$$ This is done using the distributive property, which states that $a(b+c)=ab+ac$.

   Thus, we rewrite the equation: $$2x+16=2x+8$$

2. Subtract $2x$ from both sides: $$2x+16-2x=2x+8-2x$$ Simplifying both sides yields: $$16=8$$

3. Evaluate the result: The equation $16=8$ is a false statement. This implies that there are no values of $x$ that will satisfy the original equation.

4. Conclusion: Since we arrived at a contradiction, we conclude that the equation $2(x+8)=2x+8$ has no solution.

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

Answer 2

what are the propertes and reason? and also Equation simplified