01 Key Concepts
Inequality Symbols
< (less than), > (greater than), <= (less than or equal to), >= (greater than or equal to).
Solving Like an Equation
Solve inequalities the same way as equations — using inverse operations to isolate the variable.
The Flip Rule
When multiplying or dividing both sides by a NEGATIVE number, you must flip the direction of the inequality sign.
Graphing on a Number Line
Use an open circle for < or > (the boundary value is not included) and a closed/filled circle for <= or >= (the boundary value is included).
Compound Inequalities
Combine two inequalities with AND or OR, such as -3 < x < 5, meaning x is greater than -3 AND less than 5.
02 Key Formulas
- Multiplying/dividing by a negative number flips the inequality sign
03 Solved Examples
Example 1 Solve for x: 2x + 3 > 11.
- Subtract 3 from both sides: 2x > 8.
- Divide both sides by 2: x > 4.
Answer: x > 4
Example 2 Solve for x: -3x + 6 <= 15.
- Subtract 6 from both sides: -3x <= 9.
- Divide by -3, flipping the inequality: x >= -3.
Answer: x >= -3
Example 3 Solve the compound inequality: -2 < x + 1 < 5.
- Subtract 1 from all three parts: -2-1 < x < 5-1.
- -3 < x < 4.
Answer: -3 < x < 4
04 Practice Questions
1Solve for x: 3x - 2 > 10.
x > 4
2Solve for x: -2x + 4 < 10.
x > -3
3Solve for x: 4x + 1 <= 17.
x <= 4
4Solve the compound inequality: -1 < x - 2 < 3.
1 < x < 5
5When must you flip an inequality sign?
When multiplying or dividing both sides by a negative number
📄 Linear Inequalities — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.