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KS3 Maths · Algebra · Year 7

Solving linear equations

Keep the equation balanced and undo each operation to find x.

About 20 minutes

Step 1 · Wonder why it matters

Hook

Think of a number

“I think of a number, multiply it by 3 and add 5. The answer is 26. What was my number?”

You might be able to guess this one, but what if the numbers were harder? Algebra gives you a method that always works.

Step 2 · See it

Picture

See the balance

An equation is like a set of scales in balance. Whatever you do to one side, you must do to the other, or it tips over.

  1. 3x + 5 = 26
  2. − 5 both sides
  3. 3x = 21
  4. ÷ 3 both sides
  5. x = 7

Step 3 · Understand how it works

Logic

Inverse operations

Every operation has an inverse that undoes it: + undoes −, × undoes ÷, and the other way round.

To solve an equation, undo the operations in reverse order — like taking off your shoes before your socks. The last thing done to x is the first thing you undo.

Always check by substituting your answer back into the original equation.

Equation
A statement that two expressions are equal, containing an unknown.
Inverse operation
The operation that undoes another.
Substitute
Replace a letter with a number.

Worked example

Solve 4x − 7 = 13

  1. 1The last thing done to x was “− 7”, so add 7 to both sides: 4x = 20.
  2. 2x is multiplied by 4, so divide both sides by 4: x = 5.
  3. 3Check: 4 × 5 − 7 = 20 − 7 = 13 ✓

Answer: x = 5

Step 4 · Have a go

Do

Have a go

Solve each one, showing every step, and check your answer.

  1. 1x + 9 = 15
  2. 25x = 45
  3. 32x + 3 = 17
  4. 4x/4 − 1 = 6
  5. 5Challenge: 3(x + 2) = 24 — expand the bracket first, or divide both sides by 3 first. Do both ways give the same answer?

Step 5 · Remember it

Recall

Quick quiz

Work each one out on paper first.

0 of 5 answered

  1. 1.Solve x − 8 = 12

  2. 2.Solve 6x = 42

  3. 3.Solve 3x + 4 = 19

  4. 4.What is the first step to solve x/2 + 5 = 9?

  5. 5.The hook: 3 × (number) + 5 = 26. What was the number?

Step 6 · Link it to your world

Reflect

Think about it

Equations model real situations — prices, distances, recipes.

A taxi charges £3 plus £2 per mile and the fare was £15. Write and solve an equation for the number of miles.

Saved to your notebook on this device only.

Finished all six steps?

Mark it complete to collect 3 stars. Next up: Percentages of amounts.