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 $3$ .