Solving equations
- Solving an equation means finding the value of the letter that makes it true. Do the same to both sides, using inverse operations.
- One step: x + 7 = 12, so x = 5. 4x = 20, so x = 5. x ÷ 3 = 6, so x = 18.
- Two steps: 3x + 5 = 20. Subtract 5: 3x = 15. Divide by 3: x = 5.
- Brackets: 2(x − 3) = 10. Divide by 2: x − 3 = 5, so x = 8 (or expand the bracket first).
Letters on both sides
- Get the letters on one side: 5x + 2 = 3x + 10. Subtract 3x: 2x + 2 = 10. Subtract 2: 2x = 8, so x = 4.
- Check an answer by substituting it back: 5 × 4 + 2 = 22 and 3 × 4 + 10 = 22.
Forming equations
- Write the words as an equation: "I think of a number, multiply it by 4 and subtract 3. The answer is 25." gives 4n − 3 = 25, so n = 7.
- Use facts you know: the angles in a triangle add up to 180°, and the perimeter is the sum of the sides.
Inequalities
- An inequality shows a range of values: x + 3 > 7 means x is greater than 4.
- Solve them like equations, but if you multiply or divide by a negative number, reverse the sign.
Key terms
- Equation
- A statement that two expressions are equal.
- Solve
- Find the value of the unknown letter.
- Unknown
- The letter whose value you need to find.
- Inverse operation
- The opposite operation, such as subtracting to undo adding.
- Solution
- The value that makes an equation true.
- Inequality
- A statement that one quantity is greater or less than another.