To identify the correct justification for step 3 in the solution process, let's analyze each step in detail:
1. We start with the equation:
[tex]\[
10d - 5 = 4d - 15 - 3d
\][/tex]
2. Combine like terms on the right-hand side:
[tex]\[
10d - 5 = (4d - 3d) - 15
\][/tex]
[tex]\[
10d - 5 = d - 15
\][/tex]
This is Step 1.
3. To isolate the variable [tex]\(d\)[/tex], subtract [tex]\(d\)[/tex] from both sides:
[tex]\[
10d - 5 - d = -15
\][/tex]
[tex]\[
9d - 5 = -15
\][/tex]
This is Step 2.
4. Now, we need to isolate [tex]\(d\)[/tex]. Add 5 to both sides of the equation:
[tex]\[
9d - 5 + 5 = -15 + 5
\][/tex]
[tex]\[
9d = -10
\][/tex]
This is Step 3.
The operation performed in Step 3 is the addition of 5 to both sides of the equation to isolate the term involving [tex]\(d\)[/tex]. This is an application of the addition property of equality.
Therefore, the correct justification for Step 3 is:
[tex]\[
\boxed{\text{C. the addition property of equality}}
\][/tex]
