**Further Inequalities** *KS3 Revision*

## What you need to know

**Things to remember:**

- The number on the left of > is bigger than the one on the right

6 > 3 6 is bigger than 3

- The number on the left of < is less than the one on the right

3 < 6 3 is less than 6

- The “pointy end” of the inequality “points” to the smaller number.
- The line underneath an inequality means “equals”.

There are 5 symbols we need to learn to allow us to solve inequalities:

** **

**< less than > greater than = equals**

**\leq less than or equal to [latx]\geq[/latex] greater than or equal to**

Previously we have looked at less than (<) and greater than (>).

5 < 6 5 is less than 6 6 > 5 6 is greater than 5

The focus here will be on less than or equal to \leq and \geq, but these one are a little more interesting, because they also include “equals”. Consider the follower:

5 = 5

11 = 11

These are true, 5 does equal 5, and 11 does equal 5. Our new inequalities actually include “equals” in them, so we could use them here:

5 \leq 5 5 is less than **OR **equal to 5

11 \geq 11 11 is greater than **OR** equal to 11

What would happen if we didn’t have the equals in the inequality as well?

5 < 5 5 is less than 5

11 < 11 11 is greater than 11

Well, these aren’t true, are they? These inequalities are saying that 5 IS LESS THAN 5, but this can’t be true, 5 equals 5! So, we need to be careful when we choose whether to use less than or equal to or a strict inequality.

*Note: **A strict inequality is one that doesn’t have “or equal to”.*

*Choose the numbers that satisfy the inequality y\leq7*

**7 8 4 0 2 1 10**

** **This inequality tells us that our values have to be less than OR equal to 7. So, which numbers here are smaller than 7?

**4 0 2 1**

But, remember, we have to choose “equal to” 7 as well, so 7 is included!

**7 4 0 2 1**

*Choose the integers that satisfy the inequality z\geq4.7*

**2.6 8.4 5 2 9.3 11**

*Hint:** An integer is a whole number, so we are looking for whole number that are greater than or equal to 4.7.*

* ***5 11**

## Example Questions

**Question 1:** *Choose the numbers that satisfy the inequality x\leq3*

**2.5 3.1 6.2 3 1 2**

**2.5 3 1 2**

**Question 2:** *Choose the integers that satisfy the inequality x\geq5*

**2 1 7 3 8 4 5**

**7 8 5**