Three-part inequalities on a number line
For an expression like
`-1<=x<5`
Split this into two i.e.
`-1<=x`
And
`x<5`
`-1<=x` this reads as `-1` is less than or equal to `x`
`x<5` this reads `x` is less than `5`
These can be shown on a number line as
Or as:
i.e. without an arrow.
Example 1
Write down the inequality shown in the diagram below:
Because `x` is the line between the two circles this can be read as:
The ring above `-5` shows that `-5` is less than `x`
`(-5<\x)`
The ring above `+5` shows that `x` is less than `5`
`(x<\5)`
Joining the two together
`-5<\x<5`
Answer:
`-5<\x<5`
Example 2
Write down the inequality shown in the diagram below:
Because `x` is the line between the two inequalities this can be read as
The ring above `-4` shows that `-4` is less than `x`
`(-4<\x)`
The circle above the `3` shows that `x` is less than or equal to `3`
`(x<=3)`
Joining the two together
`-4<\x<=3`
Answer:
`-4<\x<=3`
