Year 9: Linear inequalities
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1. What are linear inequalities?
A linear inequality is similar to a linear equation but instead of an equal sign, it uses an inequality symbol. These symbols include:
- < less than
- ≤ less than or equal to
- > greater than
- ≥ greater than or equal to
2. Examples of linear inequalities
- x + 3 < 7
- 2x − 5 ≥ 9
- −3x < 6
3. Solving linear inequalities
Solve them just like equations, but remember this rule:
If you multiply or divide both sides by a negative number, you must flip the inequality sign.
Example: Solve −2x > 6
Divide both sides by −2 (flip the sign): x < −3
Exercises
4. Graphing solutions on a number line
- Use an open circle for < or >
- Use a closed (filled) circle for ≤ or ≥
- Shade to the left or right depending on the inequality direction
5. Writing inequalities from word problems
Translate words into mathematical expressions:
- "at least" means ≥
- "no more than" means ≤
- "more than" means >
- "less than" means <
Example: A student must score at least 50 to pass: x ≥ 50
6. Practice questions
- Solve: x + 5 < 12
- Solve: 3x − 4 ≥ 5
- Solve and graph: −2x > 10
- Write an inequality: A person must be at least 18 years old to vote.
7. Solutions
- x < 7
- 3x ≥ 9 ⇒ x ≥ 3
- x < −5 (remember to flip the sign)
- x ≥ 18
Exercises
Practice!
Here are some exercise quizzes to further sharpen your skills in solving inequalities: