Solve the absolute value of the inequality and then write the solution in interval notation

Question

2|3x + 2| − 12 < 0

Answer 1

2|3x+2| - 12 < 0

Add 12 to both sides 2|3x+2| < 12

Divide both sides by 2 |3x+2| < 6

Now, all abs val inequalities work the same, once it is simplified to a single abs val on one side and a number on the other.

There are always 2 parts to an abs val solution. With less than, think AND - less "thand"

3x+2 < 6 AND 3x+2 > -6 NOTICE: the expression inside the vertical lines does NOT CHANGE.

What changes is the < becomes >, and the +6 becomes -6 for the second expression.

Solve each of these, keeping the AND in the solution:

Subtract 2 from both sides:

3x < 4 AND 3x > -8

Divide both sides by 3

x < 4/3 AND x > -8/3

or can write it as

-8/3 < x < 4/3