Skill: Solve one-step inequalities

An inequality compares two quantities using symbols such as $<$, $>$, $\le$, or $\ge$. To solve a one-step inequality, use the inverse operation on both sides to get the variable by itself.

Important rule: If you multiply or divide both sides by a negative number, reverse the inequality symbol.

Example

Solve:

$$-3x>12$$

Divide both sides by $-3$:

$$\frac{-3x}{-3}<\frac{12}{-3}$$

Because we divided by a negative number, the symbol changes from $>$ to $<$:

$$x<-4$$

So, the solution is all numbers less than $-4$.

On a number line, use an open circle at $-4$ because $-4$ is not included, and shade to the left.

In interval notation, the solution is:

$$(-\infty,-4)$$