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Secondary 1 · Mathematics · Algebra

Solving simple equations

Solve one- and two-step linear equations using inverse operations and check solutions by substitution.

Awaiting educator review. This material was drafted by our content team with AI assistance and is waiting for review by a qualified educator. Please check it suits your child before using it. Created 10 October 2026. How we review

These lessons were written around Australian Curriculum strands and matched to Singapore levels by age (Primary 1 is the first year of primary school). They are not aligned to MOE syllabuses or the PSLE, so check them against the syllabus your child is working towards.

Learning goals

Learners will

  • Understand an equation as a balance where both sides have the same value.
  • Solve one- and two-step linear equations using inverse operations.
  • Check a solution by substituting it back into the equation.

Success looks like

  • I can solve one-step equations such as x + 7 = 15 and 4m = 28.
  • I can solve two-step equations such as 3x − 4 = 11 by undoing the operations in reverse order.
  • I can check my answer by substituting it into the original equation.

The big idea

An equation says that two things are equal. Think of a balance scale: the left side and the right side weigh the same. To keep it balanced, whatever you do to one side, you must do to the other.

To solve an equation, we get the pronumeral on its own by using inverse operations — operations that undo each other:

  • Adding is undone by subtracting, and subtracting is undone by adding.
  • Multiplying is undone by dividing, and dividing is undone by multiplying.

One-step equations need one inverse operation. For x + 7 = 15, subtract 7 from both sides: x = 8. For 4m = 28, divide both sides by 4: m = 7.

Two-step equations have two operations. Think about how the equation was built, then undo the steps in reverse order. In 3x − 4 = 11, x was multiplied by 3 and then 4 was subtracted. So first add 4 to both sides (3x = 15), then divide both sides by 3 (x = 5). This is like taking off your shoes and socks: the shoes come off first because they went on last.

Always check your solution by substituting it into the original equation. For x = 5: 3 × 5 − 4 = 15 − 4 = 11. Both sides equal 11, so the solution is correct.

Equations can also come from word problems. Let a pronumeral stand for the unknown number, write the equation, solve it, and then answer the question in words.

Worked examples

A one-step equation

Solve x + 7 = 15.

  1. 7 has been added to x, so subtract 7 from both sides.
  2. x + 7 − 7 = 15 − 7, which gives x = 8.
  3. Check: 8 + 7 = 15. ✓

Answer: x = 8

A two-step equation

Solve 3x − 4 = 11.

  1. Undo the subtraction first: add 4 to both sides. 3x − 4 + 4 = 11 + 4, so 3x = 15.
  2. Undo the multiplication: divide both sides by 3. x = 15 ÷ 3 = 5.
  3. Check: 3 × 5 − 4 = 15 − 4 = 11. ✓

Answer: x = 5

An equation with division

Solve n ÷ 4 + 2 = 6.

  1. Subtract 2 from both sides: n ÷ 4 = 4.
  2. Undo the division by multiplying both sides by 4: n = 16.
  3. Check: 16 ÷ 4 + 2 = 4 + 2 = 6. ✓

Answer: n = 16

Practice check

Have a go, then check your answers. Each answer comes with an explanation.

  1. 1.Solve x + 9 = 14.
  2. 2.Solve 4m = 28.
  3. 3.Ali solves 2x + 5 = 17. His first step is to subtract 5 from both sides. Which equation does he get?
  4. 4.Which value of y is the solution of 3y − 2 = 13?
  5. 5.Solve y − 6 = 11.
  6. 6.Solve 5x + 3 = 38.
  7. 7.Solve a ÷ 3 − 1 = 4.
  8. 8.I think of a number, multiply it by 4 and then add 6. The answer is 34. What number did I think of?
Answer guide for parents

  1. Solve x + 9 = 14.

    x = 5 — Subtract 9 from both sides: x = 14 − 9 = 5.

  2. Solve 4m = 28.

    m = 7 — Divide both sides by 4: m = 28 ÷ 4 = 7.

  3. Ali solves 2x + 5 = 17. His first step is to subtract 5 from both sides. Which equation does he get?

    2x = 12 — 2x + 5 − 5 = 17 − 5, so 2x = 12. (Then x = 6.)

  4. Which value of y is the solution of 3y − 2 = 13?

    y = 5 — Substitute: 3 × 5 − 2 = 15 − 2 = 13. ✓ The other values do not give 13.

  5. Solve y − 6 = 11.

    y = 17 — Add 6 to both sides: y = 11 + 6 = 17. Check: 17 − 6 = 11.

  6. Solve 5x + 3 = 38.

    x = 7 — Subtract 3: 5x = 35. Divide by 5: x = 7. Check: 5 × 7 + 3 = 38.

  7. Solve a ÷ 3 − 1 = 4.

    a = 15 — Add 1: a ÷ 3 = 5. Multiply by 3: a = 15. Check: 15 ÷ 3 − 1 = 5 − 1 = 4.

  8. I think of a number, multiply it by 4 and then add 6. The answer is 34. What number did I think of?

    7 — Write 4n + 6 = 34. Subtract 6: 4n = 28. Divide by 4: n = 7. Check: 4 × 7 + 6 = 34.

Watch out for

  • Doing an operation to only one side of the equation. Use the balance-scale picture: if you take something off one side, the scales tip unless you do the same to the other side.
  • Undoing the steps in the wrong order, for example dividing 3x − 4 = 11 by 3 before adding 4 and getting the arithmetic wrong. Remind the learner to deal with the + or − first, then the × or ÷.
  • Using the same operation instead of the inverse, such as adding 7 to both sides of x + 7 = 15. Ask “What has been done to x? What undoes it?”

Tips for parents

  • Insist on a check by substitution for every answer — it builds independence because the learner can tell for themselves whether they are right.
  • Model equations with cups and counters: a cup with a hidden number of counters plus 3 loose counters balances 10 counters. How many are in the cup?
  • Encourage neat setting out with one step per line and the equals signs lined up underneath each other.

Go further

  • Make up “think of a number” puzzles for each other and solve them by writing equations.
  • Use a real balance (kitchen scales with identical small items) to model and solve an equation physically.
  • Try equations with the unknown on both sides, such as 5x + 2 = 3x + 10, by first subtracting 3x from both sides.

About 45 minutes

Make a lesson planAssign to my child

You'll need

  • Paper and pencil
  • A set of kitchen or balance scales, or a homemade coat-hanger balance (optional)
  • Small cups or envelopes and counters to model unknowns

Key words

Equation
A statement that two expressions are equal, containing an equals sign, such as 2x + 3 = 11.
Solve
To find the value of the pronumeral that makes the equation true.
Solution
The value that makes an equation true. The solution of x + 2 = 9 is x = 7.
Inverse operation
The operation that undoes another. Addition and subtraction are inverses; multiplication and division are inverses.
Substitute
To replace a pronumeral with a number to check whether the equation is true.
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