x 3 x + 3 = 8 Come play with numbers!
Two-step equations

Can we solve in two calm moves?

# Two-step practice ## Pattern A — multiply then add `5x + 2 = 17` −2 → `5x = 15` ÷5 → `x = 3` ## Pattern B — multiply then subtract `4x − 7 = 9` +7 → `4x = 16` ÷4 → `x = 4` ## Pattern C — divide then add `x/2 + 1 = 6` −1 → `x/2 = 5` ×2 → `x = 10` Write **one step per line**. Your future self (and your teacher) can follow it. ## A practice card you can copy into your notebook For `ax + b = c`: ``` ax + b = c ax = c − b x = (c − b) / a Check: put x back ``` For `ax − b = c` the middle line is `ax = c + b`. For `x/a + b = c` the last line is `x = a(c − b)`. You do not need to memorise the formula if you can say: **undo outside, then undo the multiply/divide, then check.** Do four paper problems before you touch the quiz. Speed comes after accuracy.

By the end of this lesson

Solve the three common two-step shapes (ax+b, ax−b, x/a + b) with one step per line and a check.

Remember

  • Pattern A: ax + b = c → subtract b, divide by a.
  • Pattern B: ax − b = c → add b, divide by a.
  • Pattern C: x/a + b = c → subtract b, multiply by a.
  • One step per line. Then check in the original.
  • If the check fails, the slip is usually a sign or a divide.

Worked examples

Cover the answer. Try the steps on paper, then open them.

Example 1 — Pattern A

5x + 2 = 17

  1. −2 both sides: 5x = 15
  2. ÷5: x = 3
  3. Check: 5(3)+2 = 17 ✓

Answer: x = 3

Example 2 — Pattern B

4x − 7 = 9

  1. +7 both sides: 4x = 16
  2. ÷4: x = 4
  3. Check: 4(4)−7 = 9 ✓

Answer: x = 4

Example 3 — Pattern C

x/2 + 1 = 6

  1. −1 both sides: x/2 = 5
  2. ×2: x = 10
  3. Check: 10/2 + 1 = 6 ✓

Answer: x = 10

Example 4 — Pattern B again

3x − 5 = 10

  1. +5: 3x = 15
  2. ÷3: x = 5
  3. Check: 3(5)−5 = 10 ✓

Answer: x = 5

Common mistakes

Slip 5x + 2 = 17 → x = 17 − 2 − 5 = 10

Fix You must divide the 15 by 5, not subtract 5.

After −2 you have 5x = 15.

Slip 4x − 7 = 9 → subtract 7 again to get 4x = 2

Fix The −7 is undone by +7.

9 + 7 = 16.

Slip x/2 + 1 = 6 → multiply by 2 first and drop the +1

Fix Subtract 1 first: x/2 = 5, then ×2.

Outer layer first.

Try on paper first

Write the answer, then tap Reveal. These are not the quiz — they are warm-ups.

1. 6x + 1 = 19 → x =

Answer: 3

2. 2x − 9 = 7 → x =

Answer: 8

3. x/3 + 4 = 7 → x =

Answer: 9

4. 5x − 5 = 20 → x =

Answer: 5

Touch practice

9 tap / type

Tap an option or type the answer. Retry any miss. Extra generated questions appear after the set if this topic allows it.

Optional picture lab

After practice

Real world

Pay a fee, then split the rest.

Connect

Two-step programs: subtract, then divide.

⭐ Star quiz

9 questions

Finish the touch practice first if you can. Then answer without peeking. Read every “why”.

← Two steps, reverse order All topics →