Year 10: Solve inequalities in a single variable

What is an Inequality?

An inequality is a mathematical statement that compares two expressions and shows that they are not equal. It uses symbols like < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

Steps to Solve Inequalities

1. Rewrite the inequality: Make sure the variable (usually 'x') is on its own side of the inequality.
2. Divide or Multiply by a positive number: If you multiply or divide both sides of the inequality by a positive number, the inequality sign remains the same.
3. Divide or Multiply by a negative number: If you multiply or divide both sides of the inequality by a negative number, the inequality sign must be reversed.
4. Write the solution in interval notation (recommended): This clearly represents the range of solutions.

Example

Solve: 2x + 3 < 7

1. 2x + 3 < 7
2. 2x < 4
3. x < 2
4. Solution: (–∞, 2)

Key Reminders

• Always reverse the inequality sign when multiplying or dividing by a negative number.
• Check your solution by substituting a value within the solution interval back into the original inequality.