Question

Which of the followingrepresents this line graph? ?Enter a, b, c, or d.

Answer 1

Since we need a solution which denotes a range between the points -7 and -2, the possible solutions are options a and d. Lets try with option a first.

In option a, we have the following inequality:

$|2x+9|\leq5$

which is equivalent to

$\begin{gathered} 2x+9\leq5 \\ and \\ 2x+9\ge-5 \end{gathered}$

From the first inequality, we get

$\begin{gathered} 2x\leq5-9 \\ 2x\leq-4 \end{gathered}$

then we have

$\begin{gathered} x\leq\frac{-4}{2} \\ x\leq-2 \end{gathered}$

Similarly, from the second inequality, we have

$\begin{gathered} 2x\ge-5-9 \\ 2x\ge-14 \\ then \\ x\ge\frac{-14}{2} \\ x\ge-7 \end{gathered}$

The, the inequalty given by option a:

$|2x+9|\leq5$

give us the solution

$-7\leq x\leq-2$

which corresponds to the given line.

Option d does not corresponds with the given line because the points -7 and -2 are not included on the inequality.. Threrefore, the answer is option a.