Answer:
C
Step-by-step explanation:
We have the compound inequality:
[tex]5x+7\leq-3\text{ or } 3x-4\geq11[/tex]
We will solve each inequality individually and then combine them at the end.
For the first inequality, we have:
[tex]5x+7\leq-3[/tex]
Subtract 7 from both sides:
[tex]5x\leq-10[/tex]
Divide both sides by 5:
[tex]x\leq-2[/tex]
For the second inequality, we have:
[tex]3x-4\geq11[/tex]
Add 4 to both sides:
[tex]3x\geq15[/tex]
Divide both sides by 3:
[tex]x\geq5[/tex]
Since our original inequality was an “OR,” our solution set is also an “OR.”
Hence, our solution is:
[tex]x\leq-2\text{ or } x\geq5[/tex]
Thus, our answer is C.
