To determine the correct justification for step 3 in the solution process, let's review the steps provided and understand the properties of equality used in each step.
Given equation:
[tex]\[ 0.8a - 0.1a = a - 2.5 \][/tex]
Step 1:
Combine like terms on the left side.
[tex]\[ 0.8a - 0.1a = a - 2.5 \][/tex]
[tex]\[ 0.7a = a - 2.5 \][/tex]
Step 2:
Isolate the variable [tex]\(a\)[/tex] on one side by subtracting [tex]\(a\)[/tex] from both sides.
[tex]\[ 0.7a - a = -2.5 \][/tex]
[tex]\[ -0.3a = -2.5 \][/tex]
Step 3:
Solve for [tex]\(a\)[/tex] by dividing both sides of the equation by [tex]\(-0.3\)[/tex].
[tex]\[ a = \frac{-2.5}{-0.3} \][/tex]
[tex]\[ a = 8.\overline{3} \][/tex]
In step 3, we isolated [tex]\(a\)[/tex] by performing division on both sides of the equation. This process is known as the division property of equality, which states that if you divide both sides of an equation by the same non-zero number, the two sides remain equal.
Therefore, the correct answer is:
B. the division property of equality
