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:
[tex]|2x+9|\leq5[/tex]
which is equivalent to
[tex]\begin{gathered} 2x+9\leq5 \\ and \\ 2x+9\ge-5 \end{gathered}[/tex]
From the first inequality, we get
[tex]\begin{gathered} 2x\leq5-9 \\ 2x\leq-4 \end{gathered}[/tex]
then we have
[tex]\begin{gathered} x\leq\frac{-4}{2} \\ x\leq-2 \end{gathered}[/tex]
Similarly, from the second inequality, we have
[tex]\begin{gathered} 2x\ge-5-9 \\ 2x\ge-14 \\ then \\ x\ge\frac{-14}{2} \\ x\ge-7 \end{gathered}[/tex]
The, the inequalty given by option a:
[tex]|2x+9|\leq5[/tex]
give us the solution
[tex]-7\leq x\leq-2[/tex]
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.
