To solve the compound inequality [tex]\(5x - 7 \geq 8 \text{ or } 4x + 4 < -20\)[/tex]:
### Solve the first inequality:
1. Start with [tex]\(5x - 7 \geq 8\)[/tex].
2. Add 7 to both sides:
[tex]\[
5x - 7 + 7 \geq 8 + 7 \implies 5x \geq 15
\][/tex]
3. Divide both sides by 5:
[tex]\[
\frac{5x}{5} \geq \frac{15}{5} \implies x \geq 3
\][/tex]
So, the solution to the first inequality is [tex]\(x \geq 3\)[/tex].
### Solve the second inequality:
1. Start with [tex]\(4x + 4 < -20\)[/tex].
2. Subtract 4 from both sides:
[tex]\[
4x + 4 - 4 < -20 - 4 \implies 4x < -24
\][/tex]
3. Divide both sides by 4:
[tex]\[
\frac{4x}{4} < \frac{-24}{4} \implies x < -6
\][/tex]
So, the solution to the second inequality is [tex]\(x < -6\)[/tex].
### Combine the solutions:
The overall solution to the compound inequality [tex]\(5x - 7 \geq 8 \text{ or } 4x + 4 < -20\)[/tex] is:
[tex]\[
x \geq 3 \text{ or } x < -6
\][/tex]
Thus, the correct answer is:
c. [tex]\(x \geq 3 \text{ or } x < -6\)[/tex]
