Question

Gwendolyn is asked to solve the equation −4(x−3)=20. She shows the work below and states that the solution is x=−8. −4(x−3)=20−4x+12=20−4x=32x=−8 Unfortunately, Gwendolyn's work is flawed. Explain the flaw in Gwendolyn's work. Determine the correct solution to the equation.

Answer 1

Explanation:

The equation is given as;

−4(x−3)=20

Gwendolyn's flaw is in the following lines;

−4x + 12 = 20

−4x = 32

When collecting like terms, the moment 12 crosses over, it becomes - 12 and not + 12

The correct solution is given as follows;

Step 1: Expand the brackets

This results to;

- 4x - (-4 * 3) = 20

-4x + 12 = 20

Step 2: Collect like terms

This results to;

- 4x = 20 - 12

- 4x = 8

Step 3: Solve for x

x = 8 / (-4)

x = -2