Absolute Value Equations and Inequalities

Question

Solve the compound inequality: −2 < 3x + 4 < 13 and write the solution using interval notation, then line graph your solution.

Answer 1

Hi Jonelle S.

First you need find solve for x

3x + 4 at -2 to find the low end of the interval

3x + 4 at 13 to find the high end of the interval

Keeping in mind that neither endpoint is included in the solution data set

The interval range is -2<x<3

The interval endpoints are - 2 and 3 written as (-2, 3).

The graph should show an open circle on -2 and and open circle at 3 everything in between is included

something like this

Ο—¦—0—¦—¦—Ο

You should check a couple of appropriate values in your inequality to confirm that they are correct.

Answer 2

Hi Jonelle,

Consider that the goal would be to get your inequality into the form of

# < x < #

In order to arrive at this, you'll need to change "3x + 4" into "x" somehow.

Equalities and inequalities are similar in that what you do to one part of the question you must also do to the other parts.

If you want to change "3x + 4" into "x" you would first subtract 4 from each part. Afterwards; you're left with 3x. The rest of the question will be more straightforward after this. (Hint: How would you get 3x to become "x" and be left with # < x < #?

After you have # < x < #, drawing a line graph should come naturally since you will be bound by the two different #. For interval notation, ask yourself if your bounds (both the #) can be included as solutions or not to determine whether you will be using [ ] or ( ).

Hope this helps!

-Winn