Solving Multi-Step Inequalities

A multi-step inequality is an inequality that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, or division.

To solve $$n > -2.5$$ , you isolate $$n$$ by keeping it on one side of the inequality. The solution is all values greater than -2.5.

An open circle is used when graphing $$b < 6$$ to indicate that 6 is not included in the solution.

The inequality symbol flips when you multiply or divide both sides of the inequality by a negative number.

To solve $$x - 14 < -8$$ , add 14 to both sides: $$x < 6$$ .

$$\frac{x}{-4} > 8$$ requires flipping the inequality sign because you are dividing by a negative number.

An open circle represents that the number is not included in the solution set.

A closed circle represents that the number is included in the solution set.

Subtract 5 from both sides: $$x > 5$$ .

Add 3 to both sides: $$2x < 10$$ .