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# 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?

http://static.pdesas.org/content/documents/Algebra...

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

- 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.