Year 7: Solve inequalities in a single variable

An inequality is like an equation, but instead of '=' you use symbols like > (greater than), < (less than), ≥ (greater than or equal to), or ≤ (less than or equal to).

Steps to Solve Inequalities

1. Rewrite the Inequality: Make sure the variable (e.g., 'x') is on its own side of the inequality.
2. Divide or Multiply by a Positive Number: If you divide or multiply both sides of the inequality by a positive number, the inequality sign stays the same.
3. Divide or Multiply by a Negative Number: If you divide or multiply both sides of the inequality by a negative number, the inequality sign flips (changes to > or <).
4. Check Your Solution: It’s a good idea to test a value back into the inequality to make sure your answer is correct.

Example

Solve: 2x + 1 ≥ 5

1. Subtract 1 from both sides: 2x ≥ 4
2. Divide both sides by 2: x ≥ 2

This means that x can be any number greater than or equal to 2.