Inequalities are used when a number is less than or greater than another value and will use one of the inequality signs:
< less than
≤ less than or equal to;
> greater than;
≥ greater than or equal to.
When used algebraically, the inequality will refer to a number, or range of numbers, which are either greater (or equal to), or less than (or equal to) a fixed value.
This can be shown on a number line using lines and circles. If a circle is filled, then it is equal to or greater/less than the value. If the circle is not filled, then the value is not included. A line, with an arrow, shows the range of values. Three examples are shown below:
a) `x < 3`
b) `x ≤ 3`
c) `x ≥ -2`
Two inequalities can be applied to a value at the same time. On a number line, this would be represented by a line with a circle at each end. Show, on a number line, the values of `x` that satisfy `x > -3` and `x < 5`:
1. Show, on a number line, the inequality `x > 6`.
The greater than sign indicates that the values must be greater than 6, therefore the circle must not be filled. The arrow indicates that all numbers greater than 6 are included.
2. What inequality is shown by the number line, below?
Answer: `-5 ≤ x < 0`
`x` is greater than or equal to -5; and `x` is less than 0. Note that the filled circle indicates equal to or greater than; and the circle that is not filled indicates less than.