# How do you solve the inequality #abs(x+3)>=abs(6x+9)# and write your answer in interval notation?

##### 1 Answer

#### Answer:

#### Explanation:

Solving the problem would be much easier if the absolute signs were removed. However, to do this, we need to divide the problem into cases depending on the signs of the expression inside. There are four possibilities:

**Case 1: #x+3≥0# and #6x+9≥0#**

Then the absolute signs don't really matter. We solve for

**Case 2: #x+3≥0# and #6x+9<0#**

Then, after removing the absolute signs, we must multiply the right-hand side by -1. We solve for

**Case 3: #x+3<0# and #6x+9≥0#**

Then, after removing the absolute signs, we must multiply the left-hand side by -1. We solve for

**Case 4: #x+3<0# and #6x+9<0#**

Then, after removing the absolute signs, we must multiply both sides by -1. We solve for

We combine the solutions for the cases to get