Question

Describing Steps Used to Solve an Equation with Decimals
Examine the steps used to solve the equation.

12.5x − 10.2 = 3(2.5x + 4.2) - 6

1. 12.5x − 10.2 = 7.5x + 12.6 − 6

2. 12.5x − 10.2 = 7.5x + 6.6

3. 12.5x = 7.5x + 16.8

4. 5x = 16.8

5. x = 3.36

Analyze the steps to determine which properties or procedures were used to complete each step

Step 1:
Step 2:
Step 3:
Step 4:
Step 5:

Answer 1

Step 1: Distributive property (3·(2.5x + 4.2) → 7.5x + 12.6)

Step 2: Combine like terms / simplify (12.6 − 6 → 6.6)

Step 3: Addition Property of Equality — add 10.2 to both sides (moves −10.2 to the right: 6.6 + 10.2 = 16.8)

Step 4: Subtraction Property of Equality — subtract 7.5x from both sides (12.5x − 7.5x = 5x)

Step 5: Division Property of Equality — divide both sides by 5 to isolate x (x = 16.8 ÷ 5 = 3.36)