Answer :
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]
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]
