To solve the equation \(15x - 8 = 14x + 13\), we follow several steps to isolate the variable \(x\).
First, we want to simplify the equation. We need to eliminate the constant term on the left-hand side (LHS) by performing an operation on both sides of the equation.
Here is the detailed explanation:
### Step 1
The original equation is:
[tex]\[ 15x - 8 = 14x + 13 \][/tex]
To make it simpler, we need to get rid of the \(-8\) on the LHS. We can do this by adding \(8\) to both sides of the equation. By the addition property of equality, if we add the same amount to both sides of an equation, the equality remains the same.
So, we add \(8\) to both sides to get:
[tex]\[ 15x - 8 + 8 = 14x + 13 + 8 \][/tex]
Simplifying this, we have:
[tex]\[ 15x = 14x + 21 \][/tex]
So, the operation performed in Step 1 is the addition of 8 to both sides. The justification for this step is:
D. the addition property of equality
