Inequality symbols
- < less than; > greater than; ≤ less than or equal to; ≥ greater than or equal to.
- x > 3 means x can be any number bigger than 3, but not 3 itself.
Number lines
- An open (empty) circle means the number is not included (for < and >).
- A filled (solid) circle means the number is included (for ≤ and ≥).
- For −2 < x ≤ 3, draw an open circle at −2, a filled circle at 3, and a line between them.
Solving inequalities
- Solve like an equation: 2x + 1 > 7 → 2x > 6 → x > 3.
- If you multiply or divide by a negative number, reverse the sign: −2x < 6 → x > −3.
- Double inequalities: do the same to all three parts: 5 < x + 2 ≤ 9 → 3 < x ≤ 7.
Integer solutions
- Integers are whole numbers. The integers with −2 < n ≤ 3 are −1, 0, 1, 2 and 3.
- The largest integer with 4x < 22 is 5, because x < 5.5.
- (Higher) Quadratic inequalities: x² < 16 means −4 < x < 4; x² > 16 means x < −4 or x > 4. Sketch the graph to check.
Key terms
- Inequality
- A statement that one quantity is greater or less than another.
- Integer
- A whole number: positive, negative or zero.
- Open circle
- Shows a value is not included on a number line.
- Closed circle
- Shows a value is included on a number line.
- Solution set
- All the values that make an inequality true.