Question

HELP ASAP PLS!
Solve the following and graph the solutions:
2x + 5 > - 9 or - 3x + 2 < 14
X > - 7 or x < - 4

Answer 1

Solving Compound Inequalities

Answer:

The Fourth Choice

$x > -7$

Please refer to the attached image for the graph

Step-by-step explanation:

Given:

$2x +5 > -9 \text{ or } -3x +2 < 14$

Let's solve for the $2x +5 > -9$ part of the Compound Inequality first.

$2x +5 > -9 \\ 2x > -9 -5\\ 2x > -14 \\ x > \frac{-14}{2} \\ x > -7$

Now, let's solve $-3x +2 < 14$:

$-3x +2 < 14 \\ -3x < 14 -2\\ -3x < 12 \\ x > \frac{12}{-3} \\ x > -4$

We can now rewrite our Compound Inequality as $x > -7 \text{ or } x > -4$. However, we can further simplify it by rewriting it as $x > -7$ only since the values $-7 < x \leqslant -4$ are already greater than $-7$ anyway.