Year 9: Solve inequalities in a single variable

Solving inequalities is similar to solving equations, but with one crucial difference: we're looking for a range of values, not just a single solution.

Key Steps

1. Understand the inequality symbol:
   • < (Less than) - < (e.g., x < 5)
   • > (Greater than) - > (e.g., x > 2)
   • ≤ (Less than or equal to) - ≤ (e.g., x ≤ 10)
   • ≥ (Greater than or equal to) - ≥ (e.g., x ≥ -3)
2. Isolate the variable: Add, subtract, multiply, or divide both sides of the inequality by the same non-zero number. Remember to flip the inequality sign if you divide or multiply by a negative number.
3. Write the solution in interval notation:
   • (a, b) means x can be any value greater than 'a' and less than 'b'.
   • [a, b] means x can be any value from 'a' to 'b' (including 'a' and 'b').
   • (a, ∞) means x can be any value greater than 'a'.
   • [a, ∞) means x can be any value from 'a' to &infinity.

Examples

Example 1: x + 2 < 7 => x < 5 (Solution: (-, 5))

Example 2: 3x ≥ 6 => x ≥ 2 (Solution: [2, ∞))