Solving One-Step Equations (Year 6)

A6One-Step Equations

Undo one operation to find the letter.

One-step equations solve with a single inverse operation.

Solve x + 7 = 12.

x + 7 = 12

undo + 7 → subtract 7 from both sides

x = 12 − 7 = 5

Whatever you do to one side, do to the other — the scales must stay balanced.

Learn the 3-Step Method

1See the operation on x.

x + 7 = 12: the x has had 7 added to it.

x +7

2Apply the inverse to BOTH sides.

Subtract 7 from both sides: x = 12 − 7.

−7 both sides

3Check by substituting back.

x = 5: does 5 + 7 = 12? ✓

5 + 7 = 12 ✓

💡 Key IdeaAn equation is a balance scale — take 7 off one pan only and it tips. Both sides, always.

Worked Example

Solve each equation.

x − 4 = 9

add 4 to both sides

x = 13

3x = 15

divide both sides by 3

x = 5

x ÷ 2 = 8

multiply both sides by 2

x = 16

Watch Out! Common Mistakes

Doing the same operation instead of the inverse.

x + 7 = 12 → x = 12 + 7 = 19 ✕

Inverse! Undo +7 with −7: x = 5. Check: 19 + 7 ≠ 12.

Only changing one side.

Balance! Subtracting 7 from the left only leaves the equation false. Both sides, every time.

3x = 15 → x = 15 − 3.

x = 12 ✕

Wrong inverse! 3x means 3 × x, so undo with ÷3: x = 5.

⬇ Cheat Sheet

ONE-STEP EQUATIONS

Identify the operation attached to x.
Apply the INVERSE to both sides.
+↔− and ×↔÷.
Substitute back to check.

Examples: x+7=12 → x=5 · 3x=15 → x=5 · x−4=9 → x=13.

📖 Continue Your Journey

✓ A1 What Is Algebra?✓ A2 Function Machines ✓ A3 Writing Expressions ✓ A4 Substitution ✓ A5 Simplifying Expressions A6 One-Step Equations A7 Two-Step Equations A8 Sequences A9 The nth Term A10 Formulae A11 Bar Models for Unknowns A12 Algebra Problem Solving

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Next Lesson: A7 Two-Step EquationsTwo undos, in the right order.

📄 Free printable: Download the One-Step Equations cheat sheet (PDF) — keep it by your child's desk.

Quick summary

See what operation is attached to x, then apply its inverse to both sides.
x + 7 = 12 → subtract 7 → x = 5; 3x = 15 → divide by 3 → x = 5.
The equation is a balance — never change one side only.
Always check by substituting the answer back in.

Frequently asked questions

How do you solve a one-step equation?

Undo the operation attached to the letter using its inverse, applied to both sides: x + 7 = 12 becomes x = 12 − 7 = 5.

Why must you do the same to both sides?

An equation says two sides balance. Changing only one side breaks the balance and the equality stops being true.

How can children check their answer?

Substitute it back into the original equation: x = 5 in x + 7 = 12 gives 5 + 7 = 12 ✓ — a ten-second guarantee.

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