Two-step equations

To solve a two-step equation like 3x + 7 = 22, undo the + 7 first, then the × 3. Do each step to both sides.

The idea: undo in reverse order

In 3x + 7 = 22, two things happened to x: it was multiplied by 3, then 7 was added. To get x back, undo them in reverse order.

First subtract 7 from both sides: 3x = 15. Then divide both sides by 3: x = 5. Undoing in reverse order is like taking off shoes before socks.

See it: pictures to draw with your child

Copy these onto paper or a whiteboard. A quick sketch makes the idea concrete before any written method.

xxx
3x + 2 = 14: take 2 blocks off both sides (3x = 12), then share into 3 groups (x = 4).
5× 315+ 722
Forwards: x = 5, times 3, plus 7 gives 22.
22− 715÷ 35
Backwards: undo + 7, then undo × 3. x = 5.

The two steps, every time

  1. Undo the adding or subtracting. Get the x term on its own on one side.
  2. Undo the multiplying or dividing. Get x on its own.

Then check by putting the answer back in. For 3x + 7 = 22 with x = 5: 3 × 5 + 7 = 22. It matches.

Check each step

Change the equation to see the steps. Try a negative number in front of x.

Two-step equations with negative numbers

The steps don’t change, but watch the signs. In −2x + 5 = 17, subtract 5 to get −2x = 12. Then divide by −2: x = −6.

In 4x − 9 = −1, add 9 to get 4x = 8, so x = 2. Writing every line helps keep track of each sign. See integer rules if the signs cause trouble.

Key words

Why undo in reverse order?

Think of 3x + 5 as a recipe: start with x, multiply by 3, then add 5. To get back to x, undo the last step first.

So subtract 5, then divide by 3. It is like getting dressed: socks go on before shoes, but shoes come off first.

Children who solve by undoing the multiplication first must divide every term, which is harder. Undoing in reverse keeps the numbers whole for longer.

Teaching tip: cover-up method

For 3x + 5 = 20, cover 3x with a finger and ask: “something + 5 = 20. What is the something?” It is 15.

Then 3x = 15, so x = 5. The cover-up method builds number sense before the formal steps.

Move to written inverse operations once children can explain why the cover-up works. Both methods lead to the same answer.

Ask children to say which they prefer and why. Explaining a method out loud is a strong sign it is understood.

Two-step equations in real life

Two-step equations appear whenever there is a fixed cost plus a rate. A gym charges a $10 joining fee plus $15 a month. After how many months have you paid $70?

Write 10 + 15m = 70. Subtract 10 to get 15m = 60, then divide by 15: m = 4 months.

Taxi fares, phone bills, delivery charges and savings plans all follow this pattern. Ask your child to find one in a shop or online this week.

Then change one number and solve again. What if the joining fee were $25? Seeing how the answer moves helps children understand what each part of the equation means.

Quiz: two-step equations

Undo + or − first, then × or ÷. Type a minus sign for negatives.

Where this fits: equations step by step

  1. What is an equation
  2. Variables
  3. Algebraic expressions
  4. Evaluating expressions
  5. Writing expressions
  6. Inverse operations
  7. One-step equations
  8. Combining like terms
  9. Distributive property with variables
  10. Two-step equations (this page)
  11. Equations with fractions and decimals
  12. Solving inequalities
  13. Multi-step equations
  14. Variables on both sides
  15. Systems of equations
  16. Equation word problems

What to say to your child

A short script for teaching it the first time. Pause after each line and let your child do the next step.

  1. “In 3x + 7 = 22, what was done to x?” (Times 3, then plus 7.)
  2. “What do we undo first?” (The + 7.)
  3. “Subtract 7 from both sides.” (3x = 15.)
  4. “Now undo the × 3.” (x = 5.)
  5. “Check it: 3 × 5 + 7?” (22. It works.)

More worked examples

Example 1: adding

2x + 9 = 25. Subtract 9: 2x = 16. Divide by 2: x = 8.

Example 2: subtracting

5x − 4 = 31. Add 4: 5x = 35. Divide by 5: x = 7.

Example 3: dividing

x ÷ 3 + 2 = 8. Subtract 2: x ÷ 3 = 6. Multiply by 3: x = 18.

Example 4: negative coefficient

−3x + 1 = 13. Subtract 1: −3x = 12. Divide by −3: x = −4.

Practice questions (answers below)

Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.

  1. 2x + 3 = 11
  2. 4x − 5 = 15
  3. 3x + 10 = 4
  4. x ÷ 2 + 6 = 9
  5. 6x − 1 = 29
  6. −2x + 3 = 9
  7. 5 + 2x = 19
  8. 7x + 4 = −10
  9. x ÷ 4 − 3 = 2
  10. Stretch: 0.5x + 1.5 = 4
Show the answers
  1. 4
  2. 5
  3. −2
  4. 6
  5. 5
  6. −3
  7. 7
  8. −2
  9. 20
  10. 5

Common mistakes

Dividing firstSolves 3x + 7 = 22 by dividing 22 by 3.Fix: undo the + 7 first: 3x = 15, then divide.
Dividing only part of a sideWrites 3x + 7 = 22 as x + 7 = 22 ÷ 3.Fix: get 3x on its own before dividing.
Sign slipsSolves −2x = 12 as x = 6.Fix: dividing by −2 gives x = −6.

How to teach it at home

Number machine

Your child picks a secret number, doubles it and adds 3. You work backwards to find it, then swap.

Phone plan

A plan costs $10 plus $5 a gigabyte. A bill is $35. How many gigabytes? (5)

Two-step race

Write two-step equations on cards; first to solve and check wins the card.

By grade

More for each grade: Grade 7 math and the CBSE class 7 maths guide.

Worksheets and practice

Two-step equations worksheet, page 1

Two-step equations worksheet: printable PDF with an answer key. · Make a fresh test

Equation practice · equation solver · balance scale · solving equations for kids · integers

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Questions parents ask

How do you solve a two-step equation?

Undo the adding or subtracting first, then the multiplying or dividing. Do each step to both sides.

How do you solve 3x + 7 = 22?

Subtract 7 from both sides to get 3x = 15, then divide by 3: x = 5.

Why do you undo adding before multiplying?

Because the adding was done last. Undo steps in reverse order.

Can the answer be negative?

Yes. In 3x + 10 = 4, 3x = −6, so x = −2.

What grade learns two-step equations?

Grade 7 under Common Core 7.EE.B.4a. In India, class 7 and 8.