Let's analyze the steps provided in the equation to determine the correct justification for step 2:
1. Given the equation:
[tex]\[
16 - 5x = 1 - 4x
\][/tex]
2. Subtract 1 from both sides and add 5x and 4x to both sides to get:
[tex]\[
16 - 5x - 1 + 4x = 1 - 4x - 1 + 4x
\][/tex]
which simplifies to:
[tex]\[
15 - x = 0 \quad\text{or}\quad -x = -15
\][/tex]
3. The step involves combining like terms by adding [tex]\(4x\)[/tex] on both sides of the equation:
[tex]\[
-5x + 4x = -4x + 4x - 15
\][/tex]
This yields:
[tex]\[
-x = -15
\][/tex]
Here, the operation performed is adding [tex]\(4x\)[/tex] to both sides of the equation.
The justification for this step is based on the addition property of equality, which states that you can add the same value to both sides of an equation without changing the equality.
So the correct answer is:
the addition property of equality
