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Two-Step Equation Worksheet Generator

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Learn two-step equations

A two-step equation requires two inverse operations. Undo addition or subtraction first, then undo multiplication or division.

By the end of this lesson

You will undo two operations in the right order and check the solution.

Review first if you need it: One-Step Equations, Integer Operations
01

The idea in plain English

A two-step equation has two operations wrapped around the variable. Remove the outside operation first, like taking off a coat before a shirt.

After each move, both sides must still have the same value.

02

How to recognise this kind of question

  • The variable is multiplied or divided and also has a number added or subtracted.
  • The equation usually looks like ax + b = c.
  • It takes two opposite operations to leave the variable alone.

Quick decision: Undo addition or subtraction first. Then undo multiplication or division.

03

The method

  1. Remove the added or subtracted constant from both sides.
  2. Divide or multiply both sides to isolate the variable.
  3. Check the result in the original equation.
04

Worked examples

Start here

3x + 5 = 26

  1. Subtract 5: 3x = 21.
  2. Divide by 3: x = 7.

Answer: x = 7

A little harder

−2x + 7 = 19

  1. Subtract 7 from both sides: −2x = 12.
  2. Divide both sides by −2: x = −6.
  3. Check: −2(−6) + 7 = 19.

Answer: x = −6

05

Your turn—with help

Try it

4x − 3 = 25

Need a hint?

Remove the −3 before dividing by 4.

4x − 3 + 3 = 25 + 3

Show the answer and steps
  1. Add 3 to both sides: 4x = 28.
  2. Divide both sides by 4: x = 7.
  3. Check: 4(7) − 3 = 25.

Answer: x = 7

06

Watch out for this mistake

Incorrect: 3x + 5 = 26, so x = 26 ÷ 3 − 5

Why it fails: Dividing first also divides the +5 term, so this expression does not preserve the equation.

Do this instead: Subtract 5 first, then divide by 3.

07

Quick check

Try these without looking. Then open each answer to check your thinking.

Question 1

2x + 5 = 17

Need a hint?

Subtract 5 first.

Show the answer and steps
  1. 2x = 12.
  2. x = 6.

Answer: x = 6

Question 2

3x − 8 = 10

Need a hint?

Add 8 first.

Show the answer and steps
  1. 3x = 18.
  2. x = 6.

Answer: x = 6

Question 3

−5x + 4 = 24

Need a hint?

Subtract 4, then divide by −5.

Show the answer and steps
  1. −5x = 20.
  2. x = −4.

Answer: x = −4

Remember thisRemove the loose number first; remove the coefficient second.

Common mistakes

  • Dividing before removing the constant.
  • Forgetting to perform an operation on both sides.
  • Losing a negative sign during division.

Practice tips

  • Write one balanced transformation per line.
  • Use one-step equations as a warm-up.
Free printable practice

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20 verified problemsSeed 482731
MMathBatch
Worksheet #482731
Algebra practice

Two-Step Equations

Name Date
  1. 9x − 3 = −48
  2. −6x − 8 = −50
  3. −5x − 8 = 37
  4. −3x + 11 = −4
  5. 7x − 12 = −96
  6. 9x − 12 = −111
  7. −8x + 11 = 3
  8. 5x + 14 = 39
  9. −7x − 2 = −44
  10. −6x − 2 = −62
  11. −5x − 3 = 22
  12. −6x + 5 = 77
  13. 4x + 4 = 0
  14. 9x + 2 = −25
  15. 6x − 10 = −22
  16. −3x + 13 = −17
  17. −4x + 13 = −35
  18. 7x + 1 = 43
  19. −8x − 8 = −24
  20. −7x + 13 = −57
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