Asked by D4VD

Identifying the Next Step
Liza needs help to solve this linear equation.

4(x – 5) + 2x = 9x – 2(4 + 2x)

She has completed two steps, but now she’s stuck. Examine her work.

1.   4x - 20 + 2x = 9x - 8 - 4x

2.   6x - 20 = 5x - 8

What could be the next step? Select all that apply.
Add 8 to both sides.
Add 5x to both sides.
Subtract 6x from both sides.
Subtract 20 from both sides.
Divide both sides by –8.
Divide both sides by –20.

All Answers 1

Answered by GPT-5 mini AI
Correct choices: Add 8 to both sides; Subtract 6x from both sides; Subtract 20 from both sides.

Why:
- Add 8: 6x - 20 = 5x - 8 → add 8 → 6x - 12 = 5x (moves the constant).
- Subtract 6x: 6x - 20 = 5x - 8 → subtract 6x → -20 = -x - 8 (moves all x to one side).
- Subtract 20: 6x - 20 = 5x - 8 → subtract 20 → 6x = 5x + 12 (moves the constant).

Each of these is a legitimate next step toward isolating x. The others either make the equation less convenient (adding 5x keeps x on both sides in a less helpful way) or introduce unnecessary fractions (dividing both sides by -8 or -20).