Question

Simplifying with the Distributive Property
Simplify the expression. Justify that the expressions are equivalent using x = 2.

–4(5x + 2) – 6(x – 3)


What is the simplified expression?
What is the value for both expressions when x = 2

Answer 1

Simplify:
-4(5x + 2) – 6(x – 3)
= -4·5x + -4·2 – 6·x + 6·3 (distribute)
= -20x - 8 - 6x + 18
= -26x + 10

Value when x = 2:
Original: -4(5·2 + 2) – 6(2 – 3) = -4(10 + 2) – 6(-1) = -4(12) + 6 = -48 + 6 = -42
Simplified: -26(2) + 10 = -52 + 10 = -42

Both equal -42, so the expressions are equivalent.