David correctly graphed an inequality as shown below.?

David correctly graphed an inequality as shown below.

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

The inequality David graphed was written in the form 7 ≤ ? ≤ 9.

B. What is an expression that could be put in place of the question mark so that the inequality would

have the same solution set as shown in the graph?


You can find the original question on this attached file, page 27. I would really appreciate if someone could correctly answer this! Thanks for your time...

2 Answers

  • 8 years ago
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  • 7 years ago

    The answer is x/4 + 7.5, explained to the best of my abilities as follows:

    The length of the original graph is 8, and the length of the new graph that would be from 7 to 9 is 2. Therefore, the graph was divided by four. So, starting with the original inequality of -2 < x < 6 (note that it should be less than or equal, but I don't know how to type that), you would divide all 3 parts by four to get: -2/4 < x/4 < 6/4 . From there, change to decimals by dividing and get -.5 <x/4 < 1.5. Now, we want to change the inequality from that to the one with 7 and 9 on each end. So, to change from -.5 to 7.5 (and on the other end, to change from 1.5 to 9), we would have to add 7.5 to all 3 parts of the inequality, which gives the answer as follows: 7 < x/4 + 7.5 < 9.

    In my opinion, this is too difficult for the average 9th grade Algebra I student to be doing on the Keystone Exam. I would love to see our legislators complete this question. Even though they all presumably passed Algebra I, I don't expect they had to do anything of this nature.

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