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One-step Linear Inequalities

Solving linear inequalities is very similar to linear equations. These examples will explain the parts specific to linear inequalities.

Solving Linear inequalities

- Get variable to one side, by itself
- Use inverse operation to undo what was done to the variable
- Must do the same operation to each side of the equation
- Reverse the inequality symbols when you multiply or divide with a negative number

Open dot for > and <

Closed dot for $\leq$ or $\geq$

The inequality symbol points in the direction of the arrow on the graph.

Example 1 x-3 < 5 +3 +3 Add 3 to both sides x<8 Graph:	Example 2 x+6 $\geq$ 9 -6 -6 Subtract 6 on both sides x $\geq$ 3 Graph:	Example 3 3x $\leq$ 9 ${\frac{3x}{3} }\leq {\frac{9}{3}}$ Divide 3 on both sides x $\leq$ 3 Graph:
Example 4 -x < 4 $\frac{-1x}{-1} < \frac{4}{-1}$ Divide by -1 on both sides x > -4 Graph:	Example 5 $\frac{(-10)x}{-10} \geq 2(-10)$ Divide by -10 on both sides X $\leq$ -20 Flip the inequality Graph: