Three-part inequalities

Three-part inequalities have two symbols in their expressions.

Solving a three part inequality is the same as two part inequalities. As in:

What you do to one side – You must do to the other.

Except now you do it to all three sides.

What you do on one side do on the other

Example

Solve `-4<=2x-1<=5`

So try to get `x` on its own

Add 1 to all three sides

`-4+1<=2x-1+1<=5+1`

`-3<=2x<=6`

Divide all 3 sides by 2

`(-3)/2<=(2x)/2<=6/2`

`-1.5<=x<=3`

Answer: `-1.5` is less than or equal to `x` and `x` is less than or equal to `3`.