To solve the equation [tex]\(15x - 8 = 14x + 13\)[/tex], let's consider Step 1: [tex]\(15x = 14x + 21\)[/tex].
In step 1, we need to understand how we went from [tex]\(15x - 8 = 14x + 13\)[/tex] to [tex]\(15x = 14x + 21\)[/tex].
Let's look at what was done in detail:
1. We noticed the need to isolate the terms involving [tex]\(x\)[/tex] and the constants.
2. To simplify the equation, we moved the [tex]\(-8\)[/tex] from the left side to the right side. This would be achieved by adding 8 to both sides of the equation to maintain equality:
[tex]\[
15x - 8 + 8 = 14x + 13 + 8
\][/tex]
Simplifying this:
[tex]\[
15x = 14x + 21
\][/tex]
Therefore, the justification for Step 1, moving [tex]\(-8\)[/tex] to the right side of the equation and resulting in [tex]\(15x = 14x + 21\)[/tex], follows the addition property of equality.
Thus, the correct answer is:
B. the addition property of equality.
