# Inequalities - Introduction

## (What's an Inequality?)

Inequalities are mathematical statements, which can be either true or false.
They are used to compare two quantities $$A$$ and $$B$$ to state either of the following:

• $$A$$ is greater than $$B$$.
• $$A$$ is less than $$B$$.
• $$A$$ is greater than or equal to $$B$$.
• $$A$$ is less than or equal to $$B$$.

## Inequalities - Symbols

When working with inequalities, four symbols must be known:

• $$A > B$$ : $$A$$ is greater than $$B$$.
• $$A < B$$ : $$A$$ is less than $$B$$.
• $$A \geq B$$ : $$A$$ is greater than or equal to $$B$$.
• $$A \leq B$$ : $$A$$ is less than or equal to $$B$$.

## Exercise 1

State whether each of the following statements is true or false.

1. $$2 > 5$$
2. $$7>3$$
3. $$3< 4$$
4. $$6<5$$
5. $$5 \geq 4$$
6. $$8 \geq 10$$
7. $$2 \geq 2$$
8. $$6 \leq 5$$
9. $$5 \leq 6$$
10. $$12 \leq 12$$

## Answers Without Working

1. $$2 > 5$$: False
2. $$7>3$$: True
3. $$3< 4$$: True
4. $$6<5$$: False
5. $$5 \geq 4$$: True
6. $$8 \geq 10$$: False
7. $$2 \geq 2$$: True
8. $$6 \leq 5$$: False
9. $$5 \leq 6$$: True
10. $$12 \leq 12$$: True

## Exercise 2

Complete either of the following with nothing but one of the four symbols $$>$$, $$<$$, $$\geq$$ or $$\leq$$ to make each statement true.
Note: each of these has two possible solutions, write each of the two possible solutions.

1. $$2 \quad ... \quad 7$$
2. $$10 \quad ... \quad 8$$
3. $$5 \quad ... \quad 6$$
4. $$9 \quad ... \quad 9$$
5. $$-3 \quad ... \quad 2$$
6. $$15 \quad ... \quad 13$$
7. $$-20 \quad ... \quad 1$$
8. $$0 \quad ... \quad -5$$
9. $$-10 \quad ... \quad -8$$

## Answers Without Working

1. $$2 < 7$$ and $$2 \leq 7$$
2. $$10 > 8$$ and $$10 \geq 8$$
3. $$5 < 6$$ and $$5 \leq 6$$
4. $$9 \leq 9$$ and $$9 \geq 9$$
5. $$-3 < 2$$ and $$-3 \leq 2$$
6. $$15 > 13$$ and $$15 \geq 13$$
7. $$-20 < 1$$ and $$-20 \leq 1$$
8. $$0 > -5$$ and $$0 \geq -5$$
9. $$-10 < -8$$ and $$-10 \leq -8$$

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