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
Example 2
x+6 \geq 9
-6   -6   Subtract 6 on both sides
x \geq 3
Example 3
3x \leq9
{\frac{3x}{3} }\leq {\frac{9}{3}}   Divide 3 on both sides
x \leq 3
Example 4
-x < 4
\frac{-1x}{-1} < \frac{4}{-1}   Divide by -1 on both sides x > -4
Example 5
\frac{(-10)x}{-10} \geq 2(-10)
Divide by -10 on both sides
X \leq -20 Flip the inequality