One-step equations

A one-step equation needs one move to solve: do the inverse operation to both sides. x + 5 = 12 becomes x = 7.

The idea: one move to get x alone

In a one-step equation, only one thing has been done to x. It might be adding, subtracting, multiplying or dividing.

To solve it, undo that one thing with the inverse operation. Do it to both sides so the equation stays balanced. Then x is on its own and you can read the answer.

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.

x + 5 = 12: take 5 blocks off both sides. One bag is left with 7 blocks, so x = 7.

3x = 12: share the 12 blocks into 3 equal groups. Each bag holds 4.

x ÷ 4 = 6: x was divided by 4, so multiply by 4 to get back. x = 24.

The four types of one-step equation

Adding: x + 5 = 12. Subtract 5 from both sides: x = 7.
Subtracting: x − 4 = 9. Add 4 to both sides: x = 13.
Multiplying: 3x = 21. Divide both sides by 3: x = 7.
Dividing: x ÷ 4 = 6. Multiply both sides by 4: x = 24.

Each type uses the opposite operation. See inverse operations for more on undoing.

Solve it on a balance

Take the same off both sides until one bag is left. Then try New puzzle.

Always check the answer

Put your answer back into the original equation. For x + 5 = 12 with x = 7, the left side is 7 + 5 = 12. It matches the right side, so the answer is right.

Checking takes a few seconds and catches most mistakes, especially when the inverse was done the wrong way.

Key words

Equation: a number sentence with an equals sign, like x + 4 = 9.
Variable: a letter that stands for an unknown number.
Inverse operation: the operation that undoes another: − undoes +, ÷ undoes ×.
Solution: the value that makes the equation true.
Both sides: everything left of the equals sign and everything right of it.

How to choose the inverse operation

Ask “what has been done to x?” In x + 7 = 12, 7 was added, so subtract 7. In x − 7 = 12, 7 was taken away, so add 7.

In 7x = 42, x was multiplied by 7, so divide by 7. In x/7 = 6, x was divided by 7, so multiply by 7.

Saying the question aloud each time stops children guessing. After a week of practice, the right inverse comes almost instantly.

How parents can help

Play “I’m thinking of a number”. Say “I add 6 and get 15. What is my number?” Your child answers 9, then writes x + 6 = 15.

Swap roles so your child makes up the puzzles. Making equations is just as useful as solving them.

Keep it light and quick: five puzzles in the car beat a page of sums done in tears.

One-step equations in real life

Many everyday questions are one-step equations in disguise. “I have $8 and need $15 for a game. How much more do I need?” That is 8 + m = 15, so m = 7.

“Four friends share a bill equally and each pays $9. What was the bill?” That is b ÷ 4 = 9, so b = 36.

Spotting the hidden equation is the real skill. Once children can write it, the solving takes only a moment.

Try making a list of five real questions together, then turn each one into an equation. Children remember equations they invented far better than ones from a page.

Quiz: one-step equations

Undo the one operation. Type the value of x.

Where this fits: equations step by step

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.

“What has been done to x in x + 5 = 12?” (5 was added.)
“What undoes adding 5?” (Subtracting 5.)
“Do it to both sides. What is x?” (7.)
“Now 3x = 21. What was done to x?” (Multiplied by 3.)
“So divide both sides by 3.” (x = 7.)

More worked examples

Example 1: adding

x + 8 = 15. Subtract 8: x = 7. Check: 7 + 8 = 15.

Example 2: subtracting

y − 6 = 2. Add 6: y = 8. Check: 8 − 6 = 2.

Example 3: multiplying

5n = 45. Divide by 5: n = 9. Check: 5 × 9 = 45.

Example 4: dividing

m ÷ 3 = 7. Multiply by 3: m = 21. Check: 21 ÷ 3 = 7.

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.

x + 9 = 14
x − 7 = 3
6x = 54
x ÷ 5 = 8
12 = x + 4
x + 2.5 = 7
4x = 2
x − 11 = −3
−3x = 18
Stretch: 0.25x = 6

Show the answers

5
10
9
40
8
4.5
0.5
8
−6
24

Common mistakes

Using the same operationSolves x + 5 = 12 by adding 5: x = 17.Fix: use the inverse: subtract 5, so x = 7.

Doing it to one side onlyWrites x + 5 − 5 = 12, so x = 12.Fix: subtract from both sides: x = 12 − 5 = 7.

Dividing the wrong waySolves 3x = 12 as x = 3 ÷ 12.Fix: divide the number on the other side by 3: 12 ÷ 3 = 4.

How to teach it at home

Mystery bag

Hide counters in a bag. “The bag and 3 more make 10.” Your child works out how many are inside.

Balance with cups

Use a coat-hanger balance and paper cups to act out x + 3 = 8.

Equation cards

Write ten one-step equations on cards and race to solve and check them.

By grade

Grade 6 (6.EE.B.7): solve one-step equations x + p = q and px = q with whole numbers, fractions and decimals.
Grade 7: two-step equations build on this.
In India, simple equations are part of class 7 (“Finding the Unknown”).
Next: combining like terms.

More for each grade: Grade 6 math and the CBSE class 6 maths guide.