Solving linear equations: worked examples (MYP 2–3)

To solve a linear equation, do the same operation to both sides until the letter is on its own. Undo addition and subtraction first, then multiplication and division. Always check by substituting your answer back into the original equation.

The key idea

An equation is a balance: both sides are equal. Whatever you do to one side, you must do to the other.

Work backwards through the operations. In 3x − 4 = 11, x was multiplied by 3 and then 4 was subtracted, so you add 4 first and then divide by 3.

An equation is a balance. Both sides weigh the same. Whatever you do to one side, do to the other, and it stays balanced.

To get x on its own, undo what was done to it, in reverse order: first undo the − 4 by adding 4, then undo the × 3 by dividing by 3.

Worked examples

Example 1Solve 3x − 4 = 11.
Undo in reverse order
1. 3x − 4 = 11x was ×3, then −4
2. 3x = 11 + 4Add 4 to both sides
3. 3x = 15
4. x = 15 ÷ 3Divide both sides by 3
5. x = 5Check: 3 × 5 − 4 = 11 ✓
Answer: x = 5
Example 2Solve 5(x + 2) = 2x + 19.
Brackets first, then collect x on one side
1. 5(x + 2) = 2x + 19x on both sides
2. 5x + 10 = 2x + 19Expand: 5 × x and 5 × 2
3. 3x + 10 = 19Subtract 2x from both sides
4. 3x = 9Subtract 10 from both sides
5. x = 3Check: 5 × 5 = 25 and 2 × 3 + 19 = 25 ✓
Answer: x = 3
Example 3Solve (x + 1) ÷ 4 = 3.
Undo the division first
1. (x + 1) ÷ 4 = 3x had 1 added, then ÷4
2. x + 1 = 3 × 4Multiply both sides by 4
3. x + 1 = 12
4. x = 11Subtract 1. Check: 12 ÷ 4 = 3 ✓
Answer: x = 11

Common mistakes

Expanding brackets on only the first term: 5(x + 2) is 5x + 10, not 5x + 2.
Changing the sign of a term when it hasn’t moved across the equals sign.
Skipping the check. Substituting takes seconds and catches most errors.

Practice questions

2x + 7 = 19
Show answer
x = 6
4(x − 3) = 20
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x = 8
7x − 5 = 3x + 11
Show answer
x = 4
2x ÷ 3 = 8
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x = 12