Question

solve and write interval - notation for the solution set. then graph the solution set.
2 - 4|x|> - 18
a. the solution set is \\(\left(-\infty,-\frac{7}{2}\
ight\cup\left\frac{9}{2},\infty\
ight)\\) (type your answer in interval - notation.)
b. there is no solution.
determine the correct graph of the solution set. choose the correct answer below.

Explanation:

Step1: Solve the inequality

Starting with $2 - 4x>16$. First, subtract 2 from both sides: $2-4x - 2>16 - 2$, which simplifies to $-4x>14$. Then divide both sides by - 4. When dividing an inequality by a negative number, the direction of the inequality sign changes. So we have $x<-\frac{14}{4}=-\frac{7}{2}$.

Step2: Write in interval - notation

The solution in interval notation is $(-\infty,-\frac{7}{2})$.

Answer:

The solution set in interval notation is $(-\infty,-\frac{7}{2})$. For the graph, it would be a number - line with an open circle at $-\frac{7}{2}$ and an arrow pointing to the left. Since the options are not clearly visible for graph selection in the provided image, but the correct interval notation is $(-\infty,-\frac{7}{2})$.