Integrated Math 1 / Unit 2: Equations and Inequalities
2.3 Linear Inequalities
Notes
An inequality compares expressions with $<$, $>$, $\leq$ or $\geq$. Its solution is a set of numbers, often shown on a number line.
- Solve like an equation, with one exception: reverse the inequality sign when multiplying or dividing by a negative number.
- On a number line, an open circle means the endpoint is not included ($<$, $>$); a closed circle means it is included ($\leq$, $\geq$).
- Example: $-3x + 5 > 17 \Rightarrow -3x > 12 \Rightarrow x < -4$.
Practice
Solve $-3x + 5 > 17$.
Subtract 5 to get $-3x > 12$. Dividing by $-3$ flips the sign: $x < -4$.
Solve $2(x - 4) \leq 10$.
$x - 4 \leq 5$, so $x \leq 9$. The sign stays because we divided by a positive.
A number line has a closed circle at 3 and an arrow pointing right. Which inequality does it show?
Closed circle means 3 is included, and the arrow right means larger numbers.
Ready for more? Take the Unit 2 test.