To solve the compound inequalities [tex]\(5x + 7 \leq -3\)[/tex] or [tex]\(3x - 4 \geq 11\)[/tex], let's address each inequality separately.
1. Solve the first inequality [tex]\(5x + 7 \leq -3\)[/tex]:
[tex]\[
5x + 7 \leq -3
\][/tex]
Subtract 7 from both sides:
[tex]\[
5x \leq -3 - 7
\][/tex]
[tex]\[
5x \leq -10
\][/tex]
Divide both sides by 5:
[tex]\[
x \leq \frac{-10}{5}
\][/tex]
[tex]\[
x \leq -2
\][/tex]
2. Solve the second inequality [tex]\(3x - 4 \geq 11\)[/tex]:
[tex]\[
3x - 4 \geq 11
\][/tex]
Add 4 to both sides:
[tex]\[
3x \geq 11 + 4
\][/tex]
[tex]\[
3x \geq 15
\][/tex]
Divide both sides by 3:
[tex]\[
x \geq \frac{15}{3}
\][/tex]
[tex]\[
x \geq 5
\][/tex]
The solutions from the two inequalities are:
- [tex]\(x \leq -2\)[/tex]
- [tex]\(x \geq 5\)[/tex]
Since the question asks for the compound inequality solved using the "or" condition, the overall solution is:
[tex]\[
x \leq -2 \text{ or } x \geq 5
\][/tex]
Thus, the correct option is:
D. [tex]\(x \leq -2\)[/tex] or [tex]\(x \geq 5\)[/tex]
