Linear Inequalities
Inequalities show ranges of solutions, not just single values.
Core Concept
An inequality uses <, >, <=, or >= instead of =. Solve like equations BUT flip the sign when multiplying/dividing by a NEGATIVE. x+3>7 becomes x>4. -2x<10 becomes x>-5 (flipped!). Graph on a number line: open circle for < or >, filled circle for <= or >=. Shade the direction of solutions. Compound inequalities: 2<x<8 means x is between 2 and 8.
Examples
3x+1>10: 3x>9, x>3. -4x<=20: x>=-5 (flip!). 1<2x+3<11: -2<2x<8: -1<x<4.
Solve: 2x - 5 > 3
Going Deeper
Remember: multiply or divide by a negative = FLIP the inequality sign.
Inequality Number Lines
Solve 6 inequalities. Graph each on a number line with proper open/filled circles and shading.
Inequality True/False
Given an inequality and a number, decide if it is a solution. Score points for speed and accuracy!
When do you flip the inequality sign?
-3x >= 12 becomes?
Want to keep learning?
Sign up for free to access the full curriculum — all subjects, all ages.
Start Learning Free