Table of Contents

## How do you know when to reverse the inequality symbol?

Flip the inequality sign when you multiply or divide both sides of an inequality by a negative number. You also often need to flip the inequality sign when solving inequalities with absolute values.

**Why do we reverse the inequality symbol?**

When you multiply both sides by a negative value you make the side that is greater have a “bigger” negative number, which actually means it is now less than the other side! This is why you must flip the sign whenever you multiply by a negative number.

### How do you reverse the direction of an inequality?

Multiplying each side of an inequality by a negative number reverses the direction of the inequality symbol. Dividing each side of an inequality by a negative number reverses the direction of the inequality symbol.

**Do you change the directions of the sign of a two-step inequality if the second step has a negative number?**

Sometimes, it will take more than one step to solve an inequality. Solve these problems as if there were an equals sign, but remember that if you multiply or divide by a negative number the inequality will change direction. Here is an example of a two-step inequality. Subtract 9 from both sides of the inequality.

#### How do you switch signs in inequalities?

Anytime you multiply or divide both sides of the inequality, you must “flip” or change the direction of the inequality sign. This means that if you had a less than sign <, it would become a greater than sign >.

**What are the inequality symbols?**

These inequality symbols are: less than (<), greater than (>), less than or equal (≤), greater than or equal (≥) and the not equal symbol (≠). Inequalities are used to compare numbers and determine the range or ranges of values that satisfy the conditions of a given variable.

## What are 2 step inequalities?

Two Step Inequalities are inequalities that take two steps to solve. This means that you have to add, subtract, multiply, or divide two times in order to solve the inequality. When solving each Two Step Inequality you will have to either add or subtract first and then multiply or divide second to solve the inequality.

**What are the rules for solving inequalities?**

Rules for Solving Inequalities

- Add the same number on both sides.
- From both sides, subtract the same number.
- By the same positive number, multiply both sides.
- By the same positive number, divide both sides.
- Multiply the same negative number on both sides and reverse the sign.