Compound Inequalities
Combine two inequalities using “and” or “or”.
Key idea
Combine two inequalities using “and” or “or”.
In depth
A compound inequality links two conditions with and (intersection) or or (union). Solve each part, then combine on a number line. And gives a bounded interval; or often gives two rays.
Worked example
−1 < 2x + 3 ≤ 7: subtract 3 → −4 < 2x ≤ 4; divide by 2 → −2 < x ≤ 2.
Formula
Real-world uses
- Specifying acceptable temperature or pH ranges in cooking, lab work and manufacturing
Common mistake
Mixing up and with or in the solution.
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 Compound Inequalities?
Combine two inequalities using “and” or “or”. It is a topic at the intermediate level in Algebra.
What is the formula for Compound Inequalities?
The key formula is a < x < b.
Where is Compound Inequalities used in real life?
Real-world examples: Specifying acceptable temperature or pH ranges in cooking, lab work and manufacturing.
What should I learn before Compound Inequalities?
Make sure you are comfortable with Linear Inequalities, the previous topic in Algebra.
What is a common mistake with Compound Inequalities?
Mixing up and with or in the solution.
How can I practise Compound 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 Compound Inequalities?
Move on to Absolute Value Equations 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.
- Linear Inequalities – Solve like equations but reverse the sign when multiplying by a negative.
- Absolute Value Equations – Split into two cases: inside equals ± the value.