Contents

- 1 Why do you flip the inequality sign?
- 2 What are the rules of inequalities?
- 3 Do you flip the inequality sign when you square root?
- 4 Do you switch the inequality sign when you subtract?
- 5 What are the four inequality symbols?
- 6 What is the first step to solving an inequality?
- 7 How do you simplify an inequality?
- 8 What are some real life examples of inequalities?
- 9 How do you solve absolute value inequalities?
- 10 How do you switch signs in inequalities?
- 11 How do you know if inequality is AND or OR?
- 12 When graphing do you use an open or closed circle for?

## Why do you flip the inequality sign?

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.

## What are the rules of inequalities?

When solving an **inequality**: • you can add the same quantity to each side • you can subtract the same quantity from each side • you can multiply or divide each side by the same positive quantity If you multiply or divide each side by a negative quantity, the **inequality** symbol must be reversed.

## Do you flip the inequality sign when you square root?

Since **square roots** are non-negative, **inequality** (2) is only meaningful if both sides are non-negative. Hence, squaring both sides was indeed valid. Hence, squaring **inequalities** involving negative numbers will **reverse the inequality**. For example −3 > −4 but 9 < 16.

## Do you switch the inequality sign when you subtract?

**Subtracting** the same number from each side of an **inequality does** not **change** the direction of the **inequality symbol**.

## What are the four inequality symbols?

The 4 Inequalities

Symbol | Words | Example |
---|---|---|

> | greater than |
x+3 > 2 |

< | less than | 7x < 28 |

≥ | greater than or equal to |
5 ≥ x−1 |

≤ |
less than or equal to |
2y+1 ≤ 7 |

## What is the first step to solving an inequality?

**To solve an inequality use the following steps:**

**Step**1 Eliminate fractions by multiplying all terms by the least common denominator of all fractions.**Step**2 Simplify by combining like terms on each side of the**inequality**.**Step**3 Add or subtract quantities to obtain the unknown on one side and the numbers on the other.

## How do you simplify an inequality?

Summary. Many simple **inequalities** can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own. But these things will change direction of the **inequality**: Multiplying or dividing both sides by a negative number.

## What are some real life examples of inequalities?

Situation | Mathematical Inequality |
---|---|

Speed limit | Legal speed on the highway ≤ 65 miles per hour |

Credit card |
Monthly payment ≥ 10% of your balance in that billing cycle |

Text messaging | Allowable number of text messages per month ≤ 250 |

Travel time | Time needed to walk from home to school ≥ 18 minutes |

## How do you solve absolute value inequalities?

**Here are the steps to follow when solving absolute value inequalities:**

- Isolate the
**absolute value**expression on the left side of the**inequality**. - If the number on the other side of the
**inequality**sign is negative, your equation either has no solution or all real**numbers**as solutions.

## How do you switch signs in inequalities?

The main situation where you’ll need to flip the **inequality sign** is when you multiply or divide both sides of an **inequality** by a negative number. To solve, you need to get all the x-es on the same side of the **inequality**.

## How do you know if inequality is AND or OR?

A compound **inequality** is just more than one **inequality** that we want to solve at the same time. We can either use the word ‘and’ or ‘or’ to indicate **if** we are looking at the solution to both **inequalities** (and), or **if** we are looking at the solution to either one of the **inequalities** (or).

## When graphing do you use an open or closed circle for?

When **graphing** a linear inequality on a number line, **use an open circle for** “less than” or “greater than”, and a **closed circle for** “less than or equal to” or “greater than or equal to”. The solution set for this problem **will** be all values that satisfy both -3 < x and x < 4.