3.5 Inequalities

State the meaning of the following inequalities.

1.

$x<10$

$x$ is less than 10.

2.

$x>10$

$x$ is greater than 10.

3.

$y\le 4$

$y$ is less than or equal to 4.

4.

$y\ge 90$

$y$ is greater than or equal to 90.

5.

$3<a\le 10$

$a$ is greater than 3 but less than or equal to 10.

6.

$-4\le a<-1$

$a$ is greater than or equal to -4 but less than -1.

7.

$60\ge x\ge -10$

$x$ is less than or equal to 60 but greater than or equal to -10.

## Inequality Symbols

It is very easy to get the symbol round the wrong way. **So always check**.

If the letter (say $x$) is next to the bigger end of the symbol ($x>$) then **$x$ is greater than…**

If the letter (say $x$) is next to the little end of the symbol ($x<$) then **$x$ is less than…**

The symbol with the double line (i.e. $\le $ or $\ge $) is inclusive of the value (hence equal to).