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

Which of the followingrepresents this line graph? ?Enter a, b, c, or d.-example-1

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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.

User Iqbal Kabir
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