Question

How do you solve and graph the compound inequality `2x - 6 < -14` or `2x + 3 < 1` ?

Answer 1

Solve compound inequalities.
(1) 2x - 6 < - 14
(2) 2x + 3 < 1

Explanation:

(1) 2x - 6 < -14 -> 2x < - 8 -> x < - 4

(2) 2x + 3 < 1 -> 2x < -2 --> x < -1

Compound solution set: x < - 4

==========|-4----------|-1-------|0----------------

Answer 2

To solve any complex inequality you solve each inequality separately and then if the problem says "or" then you combine the 2 answers since only one of the two inequalities needs to be true. (If the problem says "and" then the solutions is were the two graphs would over lap, since both inequality need to be true.

Explanation:

I created a video to help explain this at:
http://www.frontporchmath.com/topic/compound-inequalities/

this is my website: FrontPorchMath.com