Inequalities · Grade 10
In Grade 10 you learn: quadratic inequalities.
An inequality compares two values: < less than, > greater than, ≤ less than or equal to, ≥ greater than or equal to. Solving one gives a range of answers rather than a single value — like “you must be at least 120 cm tall to go on this ride”.
Key facts
- x > 3 means any number bigger than 3, but not 3 itself; x ≥ 3 includes 3.
- On a number line, use an open circle for < or > and a filled circle for ≤ or ≥.
- Solve like an equation: add, subtract, multiply or divide both sides.
- Multiplying or dividing by a negative number reverses the sign: −2x < 6 gives x > −3.
- For a double inequality like −1 < 2x + 3 ≤ 9, do the same to all three parts.
- x² < 9 gives −3 < x < 3, but x² > 9 gives x < −3 or x > 3.
Worked examples
Example 1
List the integers that satisfy −3 ≤ n < 2.
Answer: −3, −2, −1, 0, 1
Example 2
Solve x² − 2x − 3 < 0.
Answer: −1 < x < 3