To solve the equation \( 2(x+8) = 2x + 8 \) and justify each step, we can follow these steps:
Step 1: Distributive Property
Apply the distributive property to the left side of the equation.
\[ 2(x+8) = 2 \cdot x + 2 \cdot 8 \]
This simplifies to:
\[ 2x + 16 = 2x + 8 \]
Step 2: Subtraction Property of Equality
Next, we can subtract \( 2x \) from both sides of the equation.
\[ 2x + 16 - 2x = 2x + 8 - 2x \]
This simplifies to:
\[ 16 = 8 \]
Reasoning
The first step uses the Distributive Property to expand \( 2(x+8) \). The second step uses the Subtraction Property of Equality, which states that if two quantities are equal, subtracting the same amount from both sides maintains equality.
Conclusion
Now, we see that \( 16 = 8 \) is a false statement. This indicates that there are no values of \( x \) that will satisfy the original equation.
Thus, for this equation, there is no solution.