Let's go through the equation step by step and justify each step with the correct reasoning.
The original equation is:
\[ 2(x + 8) = 2x + 8 \]
Step 1: Apply the Distributive Property to get the simplified equation:
\[ 2 \cdot x + 2 \cdot 8 = 2x + 8 \]
This simplifies to:
\[ 2x + 16 = 2x + 8 \]
Step 2: Now, we will apply the Subtraction of Equality property to isolate terms. We can subtract \(2x\) from both sides of the equation:
\[ 2x + 16 - 2x = 2x + 8 - 2x \]
This simplifies to:
\[ 16 = 8 \]
At this point, we see that 16 does not equal 8, indicating that there are no solutions for this equation.
Properties and Reasons:
- Step 1: Distributive Property to get \(2x + 16 = 2x + 8\)
- Step 2: Subtraction of Equality to get \(16 = 8\)
For this equation, there is/are no solution.
Final summary:
- We started with \(2(x + 8) = 2x + 8\).
- After applying the Distributive Property, we got \(2x + 16 = 2x + 8\).
- After applying the Subtraction of Equality, we arrived at \(16 = 8\), which is a contradiction (always false), thus indicating that there are no solutions to the equation.