Question

Solve the equation. Check for extraneous solutions.

9|9 – 8x|=2x+3

Answer 1

I would suggest, for questions like this, using an algebra calculator.

Answer 2

You first get rid of the absolute values by substituting in the definition.
|x| = (x) if x >= 0 but |x| = -(x) if x < 0
9-8x < 0 if x > 9/8 so you have two separate cases:
If x> 9/8, then - 9(9 - 8x) = 2x + 3 so -81 + 72x = 2x + 3 so 70x = 84 and x = 1.2
If we check 9 - 8(1.2) is in fact < 0 so that is a good answer.
If x 0 so that is a good answer also