# How do you solve and write the following in interval notation: #4+abs(3x+2) <=5#?

##### 1 Answer

#### Explanation:

The absolute value function

We will use this definition to consider all possible cases.

**Case 1:**

Note that for this to occur, we must have

Now, by the definition of the absolute value function, we have

*Recall that when multiplying or dividing by a positive number, the direction of the inequality stays the same, and when multiplying or dividing by a negative number, we change the direction of the inequality*

So, together with the initial restriction

or, in interval notation,

**Case 2:**

As above, we first solve for

By the definition of the absolute value function, in this case we have

*We multiplied by #-1# in the prior step, and so reversed the direction of the inequality.*

Together with the initial restriction of

or, in interval notation,

If we look at where the intervals of the solutions of each case lay, we find that they meet at and include

or, in interval notation,