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An inequality is shown below: −np − 5 ≤ 4(c − 2) Which of the following solves for n?

Select one:
a. n ≥ − the quantity 4 times c minus 3 all over p
b. n ≥ − the quantity 4 times c minus 13 all over p
c. n ≤ − the quantity 4 times c minus 3 all over p
d. n ≤ − the quantity 4 times c minus 13 all over p

The answer is choice A

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Work Shown:

[tex]-np - 5 \le 4(c-2)[/tex]

[tex]-np - 5+5 \le 4(c-2)+5[/tex] Adding 5 to both sides

[tex]-np \le 4(c-2)+5[/tex]

[tex]-np \le 4(c)+4(-2)+5[/tex] Distributive Property

[tex]-np \le 4c-8+5[/tex]

[tex]-np \le 4c-3[/tex]

[tex]n*(-p) \le 4c-3[/tex]

[tex]\frac{n*(-p)}{-p} \ge \frac{4c-3}{-p}[/tex] See note below

[tex]n \ge -\frac{4c-3}{p}[/tex]

So that's why the answer is choice A

Note: In this step, I divided both sides by -p. Dividing both sides of an inequality by a negative number will flip the sign. So that's why we go from a "less than or equal to" sign to a "greater than or equal to" sign.