# 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.

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.