Sure, let's walk through the justification for the steps given in the equation.
Starting with the initial equation:
[tex]\[ 10x - 25 - 3x = 4x - 1 \][/tex]
Step 1: Simplify the left side of the equation by combining like terms.
[tex]\[ 10x - 3x - 25 = 4x - 1 \][/tex]
[tex]\[ 7x - 25 = 4x - 1 \][/tex]
So far, this simplification process is straightforward and doesn't require any specific property of equality; we just combined like terms.
Step 2: To move from step 1 to step 2, we need to isolate the term involving `x` on one side of the equation. In doing so, we look at the equation:
[tex]\[ 7x - 25 = 4x - 1 \][/tex]
We want to eliminate the [tex]\(-25\)[/tex] on the left side. To achieve that, we add [tex]\(25\)[/tex] to both sides of the equation:
[tex]\[ 7x - 25 + 25 = 4x - 1 + 25 \][/tex]
[tex]\[ 7x = 4x + 24 \][/tex]
The property used here is the addition property of equality, which states that the same value can be added to both sides of an equation without changing the equality.
Therefore, the correct justification for the transition from Step 1:
[tex]\[ 7x - 25 = 4x - 1 \][/tex]
to Step 2:
[tex]\[ 7x = 4x + 24 \][/tex]
is:
[tex]\[ \boxed{D \text{. the addition property of equality}} \][/tex]
