1 Answer

Denis Washington · Answer 1 · 2022-01-20T15:21:17+0000

Solving Compound Inequalities

The third Choice

$x > 1 \text{ or } x < -1$

Please refer to the attached image for the graph

Given:

$2x +1 > 3 \text{ or } 2x -1 < -3$

Let's solve for the
2x +1 > 3 part of the Compound Inequality first.

$2x +1 > 3 \\ 2x > 3 -1 \\ 2x > 2 \\ x > (2)/(2) \\ x > 1$

Now, let's solve
2x -1 < -3 :

$2x -1 < -3 \\ 2x < -3 +1 \\ 2x < -2 \\ x < (-2)/(2) \\ x < -1$

We can now rewrite our Compound Inequality as
$x > 1 \text{ or } x < -1$