Question

Verifying a Simplified Expression
Ranger wants to verify that the expression

8x – 20 is the correct simplified expression for 4(2x – 5). Explain how to verify the simplified expression.

Answer 1

Use the distributive property: multiply 4 by each term inside the parentheses.

4(2x − 5) = 4·2x − 4·5 = 8x − 20.

You can also check by factoring back or by testing values. Factoring: 8x − 20 = 4(2x − 5). Numeric check: let x = 0 → 4(2·0 − 5) = 4(−5) = −20 and 8·0 − 20 = −20; let x = 2 → 4(4 − 5) = 4(−1) = −4 and 8·2 − 20 = 16 − 20 = −4. Since the algebra and tests agree, 8x − 20 is the correct simplification.