Algebra · Quick Reference

Linear Inequalities Cheat Sheet

Algebra I · Lesson 2/17

In one line: a linear inequality compares two expressions using less than, greater than, or their 'or equal to' versions — describing a whole range of possible solutions instead of just one.

Key Ideas

1Inequality Symbols. < (less than), > (greater than), <= (less than or equal to), >= (greater than or equal to).

2Solving Like an Equation. Solve inequalities the same way as equations — using inverse operations to isolate the variable.

3The Flip Rule. When multiplying or dividing both sides by a NEGATIVE number, you must flip the direction of the inequality sign.

4Graphing 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).

5Compound Inequalities. Combine two inequalities with AND or OR, such as -3 < x < 5, meaning x is greater than -3 AND less than 5.

Worked Examples

Solve for x: 2x + 3 > 11.

x > 4

Solve for x: -3x + 6 <= 15.

x >= -3

Solve the compound inequality: -2 < x + 1 < 5.

-3 < x < 4

Formulas

Multiplying/dividing by a negative number flips the inequality sign

Practice Yourself

Solve for x: 3x - 2 > 10.

x > 4

Solve for x: -2x + 4 < 10.

x > -3

Solve for x: 4x + 1 <= 17.

x <= 4