Mathematics (Core)Exam code: 0580
Linear Equations
Algebra and Sequences
Brackets
- Expand the bracket first, then solve as usual
- 3(2x + 5) = 39 expands to 6x + 15 = 39, giving 6x = 24 and x = 4
- Dividing through by the number outside also works, though it can create fractions
Fractions
- Multiply both sides by the denominator, so no term is left divided
- x/4 = 3 gives x = 12, and 2x/5 = 6 gives 2x = 30, so x = 15
- Terms without a denominator must be multiplied too, which is the step most often missed
Unknowns on both sides
- Remove the smaller unknown term by applying its inverse to both sides, which avoids negatives
- 7x − 4 = 2x + 21 becomes 5x − 4 = 21 after subtracting 2x
- Then 5x = 25 and x = 5
Worked example
Unknowns on both sides
Solve (a) 3(2x − 5) = 4x + 9, (b) 5y − 9 = 23 − 3y.
Solution:
- (a) Expand the bracket first: 6x − 15 = 4x + 9
- 4x is the smaller unknown term, so subtract 4x from both sides: 2x − 15 = 9
- Add 15 to both sides: 2x = 24
- x = 12
- Check: 3(2 × 12 − 5) = 3 × 19 = 57, and 4 × 12 + 9 = 57
- (b) The unknown term on the right is −3y, so add 3y to both sides: 8y − 9 = 23
- Add 9 to both sides: 8y = 32
- y = 4
- Check: 5 × 4 − 9 = 11, and 23 − 3 × 4 = 11