# How do you solve #abs((2x+1) / (x-3))> 3#?

##### 2 Answers

Everything except 3.

#### Explanation:

This means that either:

Multiplying both sides by (x-3) gives us

Which simplifies to

And now we can algebraically reduce this to get a simple answer.

In simple terms (I like simple),

#### Explanation:

with exclusion

So we are looking for:

[1]:

or

[2]:

In case [1] first subtract

If

So **reverse the inequality** to get:

Add

Divide both sides by

So case [1] gives us the solution

In case [2] first subtract

We require

Multiply both sides of the inequality by

Add

So case [2] gives us the solution

In general you can do any of the following to an inequality and preserve its truth:

(1) Add or subtract the same value on both sides of the inequality.

(2) Multiply or divide both sides of the inequality by the same positive value.

(3) Multiply or divide both sides of the inequality by the same negative value and **reverse the inequality** (

graph{(y-abs((2x+1)/(x-3)))*(y-3) = 0 [-17.74, 22.26, -6.8, 13.2]}