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

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 > (-14)/(2) \\ x > -7`

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

`-3x +2 < 14 \\ -3x < 14 -2\\ -3x < 12 \\ x > (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.