Linear Inequalities
Solve like equations but reverse the sign when multiplying by a negative.
Key idea
Solve like equations but reverse the sign when multiplying by a negative.
In depth
An inequality has a solution set, not a single value. Solve like an equation, but multiplying or dividing by a negative reverses the inequality sign because it flips the order on the number line.
Worked example
−2x + 3 < 9: −2x < 6; divide by −2 and flip: x > −3.
Formula
Real-world uses
- Setting a spending limit
- Finding how many hours a student must study to reach a target score
Common mistake
Forgetting to flip the sign when dividing by a negative.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Linear Inequalities?
Solve like equations but reverse the sign when multiplying by a negative. It is a topic at the intermediate level in Algebra.
What is the formula for Linear Inequalities?
The key formula is −2x > 6 ⇒ x < −3.
Where is Linear Inequalities used in real life?
Real-world examples: Setting a spending limit; Finding how many hours a student must study to reach a target score.
What should I learn before Linear Inequalities?
Make sure you are comfortable with Identity and No-Solution Equations, the previous topic in Algebra.
What is a common mistake with Linear Inequalities?
Forgetting to flip the sign when dividing by a negative.
How can I practise Linear Inequalities?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Linear Inequalities?
Move on to Compound Inequalities next.
Related intermediate topics in Algebra
- Multi-Step Equations – Distribute, combine like terms, move variables to one side.
- Variables on Both Sides – Collect variable terms on one side first.
- Literal Equations – Rearrange formulas to solve for a chosen variable.
- Identity and No-Solution Equations – Some equations are always true or never true.
- Compound Inequalities – Combine two inequalities using “and” or “or”.
- Absolute Value Equations – Split into two cases: inside equals ± the value.