 Further Inequalities Revision | KS3 Maths Resources

## 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

2.5 3 1 2

7 8 5

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