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(-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(-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.