Question

value: 3
solve and graph. select all answers that
-3(4n + 2) < -78
mark all correct answers
a. n > -22
b. n > 6
c. n > -14
d. number line with -22, -20, -18, -16, -14, -12
e. number line with 4, 6, 8, 10, 12
f. number line with -20, -18, -16, -14, -12, -10

Explanation:

Step1: Expand the left - hand side

$$-3(4n + 2)=-12n-6$$
The inequality becomes $-12n - 6\lt-78$.

Step2: Add 6 to both sides

$$-12n-6 + 6\lt-78 + 6$$
$$-12n\lt-72$$

Step3: Divide both sides by - 12 (and reverse the inequality sign)

When dividing an inequality by a negative number, the inequality sign flips.
$$n\gt\frac{-72}{-12}$$
$$n\gt6$$

The graph of $n\gt6$ has an open circle at 6 (since the inequality is strict, $n
eq6$) and the line extends to the right.

Answer:

B. $n > 6$, E. (the graph with an open circle at 6 and extending to the right)