Question

Esma and Hunter were trying to solve the equation: −8x=2x−8. They both agreed they should first subtract 2x and add 8 to both sides and rewrite the equation as −6x+8=0. Then Esma said, "I can complete the square. I can add 1 to both sides to rewrite this equation as −6x+9=1, factor, and solve using square roots." Hunter said, "I'll factor the left-hand side of the equation as (x−2)(x−4) and solve using the zero product property." Whose solution strategy would work?

Options:
A) Only Esma's
B) Only Hunter's
C) Both
D) Neither

Answer 1

Both Esma's and Hunter's solution strategies would work.

Step-by-step explanation:

Both Esma's and Hunter's solution strategies would work.

Esma's strategy involves completing the square by adding 1 to both sides of the equation to rewrite it as -6x+9=1. She can then factor the left-hand side of the equation as (x-2)(x-4) and solve using the zero product property. This would give her the values of x that satisfy the equation.

Hunter's strategy involves factoring the left-hand side of the equation as (x-2)(x-4), applying the zero product property, and solving for x. This would also give him the values of x that satisfy the equation.