Lesson: Solving Two-Step Equations (Grade 7)

An equation is a balanced scale. Whatever you do to one side, do to the other side too.

The mystery box

In 3x + 5 = 20, each x is a box with a secret number inside. We have 3 boxes and 5 extra. Together they weigh the same as 20.

Solve 3x + 5 = 20 in 2 steps

Step 1: get rid of the extra 5. Take 5 away from both sides.

3x + 5 − 5 = 20 − 5 → 3x = 15

Step 2: find one box. 3 boxes weigh 15. Share 15 by 3.

15 ÷ 3 = 5 → x = 5

Check it

Put 5 back in the boxes: 3 × 5 + 5 = 15 + 5 = 20. ✔ It balances!

The "undo" rule

To find x, undo what was done to it. Use the opposite:

Undo the plus or minus first, then the times or divide. It's like getting undressed: shoes come off before socks!

Two more examples

x/4 − 2 = 6

1. Undo the − 2: add 2 to both sides → x/4 = 8
2. Undo the ÷ 4: multiply both sides by 4 → x = 32

Check: 32 ÷ 4 − 2 = 8 − 2 = 6 ✔

2x − 3 = 11

1. Undo the − 3: add 3 to both sides → 2x = 14
2. Undo the × 2: divide both sides by 2 → x = 7

Check: 2 × 7 − 3 = 14 − 3 = 11 ✔

Practice

Try Two-Step Equations & Inequalities. If that feels hard, start with One-Step Equations.