To understand the justification for step 3 in the solution process, let's break down each step and see how we progress from one to the next:
Step 1: Simplify the left side of the original equation.
[tex]\[ 0.8a - 0.1a = a - 2.5 \][/tex]
Combining like terms (combining [tex]\(0.8a\)[/tex] and [tex]\(-0.1a\)[/tex]) we get:
[tex]\[ 0.7a = a - 2.5 \][/tex]
Step 2: Move all terms involving [tex]\(a\)[/tex] to one side of the equation. To do this, we can subtract [tex]\(a\)[/tex] from both sides.
[tex]\[ 0.7a - a = -2.5 \][/tex]
Simplifying the left side:
[tex]\[ -0.3a = -2.5 \][/tex]
Step 3: Isolate [tex]\(a\)[/tex] by dividing both sides of the equation by the coefficient of [tex]\(a\)[/tex], which is [tex]\(-0.3\)[/tex].
[tex]\[ a = \frac{-2.5}{-0.3} \][/tex]
Performing the division:
[tex]\[ a = 8.\overline{3} \][/tex]
The operation used in Step 3 is division, specifically dividing both sides of the equation by the coefficient of [tex]\(a\)[/tex] to isolate [tex]\(a\)[/tex].
Therefore, the justification for Step 3 is:
[tex]\[ B. \text{the division property of equality} \][/tex]
