Question

Which are solutions of the equation 4x2 – 7x = 3x + 24? Check all that apply.

x = –4
x = –3
x = - 3/2
x = 2/3
x = 2
x = 4

If possible, please include the explanation using the GCF, factoring, and grouping. Thank you!

Answer 1

x = -3/2, x = 4

Explanation:

4x² - 7x = 3x + 24, first put everything on one side

4x² - 10x - 24 = 0, factor 2 out

2(2x² - 5x - 12) = 0 then factor. You need two numbers that multiply to be -24 and add to be -5, so -8 and 3 are the factors.

(2x² - 8x) + (3x - 12) group them either way and then factor out GCF

2x(x - 4) + 3(x - 4) = 0

(2x + 3)(x - 4) = 0, set each factor = 0 and solve

2x + 3 = 0, 2x = -3, x = -3/2

x - 4 = 0, x = 4