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

Answer

2.5       3          1          2

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

 

2          1          7          3          8          4          5

Answer

7          8          5