Linear Inequalities
A free College Algebra lesson from the “Linear Equations and Inequalities” unit, with a worked example and practice problems including step-by-step solutions.
A linear inequality compares two expressions instead of setting them equal. Its solution is usually a range of values rather than one number. You solve linear inequalities much like equations, but if you multiply or divide both sides by a negative number, the inequality symbol reverses. This matters because inequalities model limits, budgets, minimum requirements, and intervals. When practicing, isolate the variable, track the direction of the symbol, and interpret the answer as a set of allowed values. A common mistake is forgetting to flip the symbol after dividing by a negative coefficient.
What you'll learn
- Solve linear inequalities
- Know when to reverse the inequality sign
- Interpret solution intervals
Worked example
Problem. Solve -3x + 4 < 19.
- Subtract 4: -3x < 15.
- Divide by -3 and reverse the sign.
- x > -5.
Answer: x > -5
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Solve x + 9 < 15. Enter the boundary number.
Show solution
- Subtract 9.
Answer: 6
2. Solve 4x >= 28. Enter the boundary number.
Show solution
- Divide by 4.
Answer: 7
3. Solve -2x <= 10. Enter the boundary number.
Show solution
- Divide by -2 and reverse the inequality.
Answer: -5
4. Solve 2x - 7 <= 11. Enter the boundary number.
Show solution
- Add 7, then divide by 2.
Answer: 9
5. Solve -5x + 3 > 28. Enter the boundary number.
Show solution
- Subtract 3, then divide by -5 and reverse the sign.
Answer: -5
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