Solving equations
- An equation stays balanced if you do the same to both sides. Use inverse operations to get the unknown on its own.
- One step: x + 7 = 12 → x = 5; 4x = 28 → x = 7.
- Two steps: 3x − 5 = 16 → 3x = 21 → x = 7.
Unknowns on both sides
- Collect the unknowns on the side with more of them: 5x + 2 = 3x + 10 → 2x = 8 → x = 4.
- 7 − 2x = 1 → 6 = 2x → x = 3.
Brackets and fractions
- Expand brackets first: 2(x + 3) = 14 → 2x + 6 = 14 → x = 4.
- Multiply both sides to clear fractions: x/3 = 6 → x = 18; (x + 4)/2 = 5 → x + 4 = 10 → x = 6.
- (2x − 1)/3 = x − 2 → 2x − 1 = 3x − 6 → x = 5.
Forming equations
- Use a letter for the unknown and write an equation from the information: 'I think of a number, multiply by 3 and add 4 to get 25' gives 3n + 4 = 25, so n = 7.
- Angles in a triangle x, 2x and 3x: 6x = 180, so x = 30.
- Always check by substituting your answer back in.
Key terms
- Equation
- A statement that two expressions are equal.
- Solve
- Find the value of the unknown that makes the equation true.
- Unknown
- The letter whose value you are finding.
- Inverse operation
- An operation that undoes another.
- Balance method
- Doing the same to both sides so the equation stays true.