# How do you graph the compound inequality #3p+6<8-p# and #5p+8>=p+6#?

##### 1 Answer

The first step is to bring both inequalities to a simplest possible form using invariant transformations (that is, those that produce equivalent inequalities).

Add

Divide both sides by

Subtract

Divide both sides by

Now it's easy to combine both simplified inequalities (1) and (2).

The first one restricts

The second one restricts

Combining these restrictions, we come to an interval

Graphically, it is represented by an interval on the X-axis

Usually, an arrow on the side of strong inequality (

graph{sqrt(x+1/2)*0+sqrt(1/2-x) *0 [-1, 1, -0.5, 0.5]}