Lesson 7: Inequalities
An inequality shows a relationship between two expressions that are not necessarily equal. Instead of one exact answer, inequalities have a range of solutions.
Key Concepts
Inequality Symbols
< less than. > greater than. ≤ less than or equal to. ≥ greater than or equal to. ≠ not equal to. x > 3 means x can be 4, 5, 100, 3.1, — any number greater than 3.
Solving Inequalities
Same steps as equations, EXCEPT: when you multiply or divide by a NEGATIVE number, flip the inequality sign! 3 > 1, multiply by -1: -3 < -1. The direction flips.
Graphing on a Number Line
Open circle (◦) for < or > (does not include the endpoint). Closed circle (•) for ≤ or ≥ (includes the endpoint). Arrow pointing in the direction of solutions.
Compound Inequalities
AND: -2 < x ≤ 5 (between -2 and 5, including 5). OR: x < -1 or x > 4 (less than -1 OR greater than 4). AND narrows the solution set; OR widens it.
🔬 Interactive Lab: Inequalities Lab
✅ Check Your Understanding
1. Solve: -2x > 8. What happens to the inequality sign?
2. Which symbol means 'greater than or equal to'?
3. On a number line, x ≤ 4 is shown with: