Let's analyze the given equation step-by-step and determine the justification for step 3.
Given equation:
[tex]\[
0.8a - 0.1a = a - 2.5
\][/tex]
Step 1: Combine the like terms on the left side.
[tex]\[
(0.8 - 0.1)a = 0.7a
\][/tex]
This simplifies the equation to:
[tex]\[
0.7a = a - 2.5
\][/tex]
Justification: C. combining like terms
Step 2: To isolate the term involving [tex]\( a \)[/tex] on one side, we subtract [tex]\( a \)[/tex] from both sides:
[tex]\[
0.7a - a = -2.5
\][/tex]
Simplify the left side by combining like terms:
[tex]\[
(0.7 - 1)a = -0.3a
\][/tex]
Thus, the equation becomes:
[tex]\[
-0.3a = -2.5
\][/tex]
Justification: B. the subtraction property of equality
Step 3: To solve for [tex]\( a \)[/tex], we divide both sides by [tex]\( -0.3 \)[/tex]:
[tex]\[
a = \frac{-2.5}{-0.3}
\][/tex]
Simplify the fraction:
[tex]\[
a = \frac{2.5}{0.3} = 8.33 \text{ or } 8. \overline{3}
\][/tex]
Justification: D. the division property of equality
Therefore, the correct justification for step 3 is:
[tex]\[
\boxed{D. \text{the division property of equality}}
\][/tex]
