Question

what is the justification for step 3 in the solution process?
0.8a - 0.1a = a - 2.5
step 1: 0.7a = a - 2.5
step 2: -0.3a = -2.5
step 3: a = 8.\overline{3}
a. the addition property of equality
b. combining like terms
c. the division property of equality
d. the subtraction property of equality

Explanation:

To find the justification for Step 3, we analyze the transition from Step 2 ($-0.3a = -2.5$) to Step 3 ($a = 8.\overline{3}$). The division property of equality states that if we divide both sides of an equation by the same non - zero number, the equation remains true. In Step 3, we divide both sides of the equation $-0.3a=-2.5$ by $- 0.3$ (or multiply both sides by $\frac{1}{-0.3}$) to solve for $a$.

• Option A: The addition property of equality involves adding the same number to both sides, which is not what happened here.
• Option B: Combining like terms is done when we simplify expressions by adding or subtracting like terms, which was done in Step 1, not Step 3.
• Option D: The subtraction property of equality involves subtracting the same number from both sides, which is not the operation used in Step 3.

So the correct justification is the division property of equality.

Answer:

C. the division property of equality