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Question 549975: A solution to the compound inequality 17 <= 3 - 2x <= 21 is given below. Choose the statement that is true about the given solution.
17 <= 3 - 2x and 3 - 2x <= 21 - Line 1
20 <= -2x and -2x <= 24 - Line 2
-10 => x and x => -12 - Line 3
A: There is a mistake in line # 1.
B: There is a mistake in line # 2.
C: There is a mistake in line # 3.
D: There are no mistakes, the solution is correct.
Answer by karaoz(32)   (Show Source):
You can put this solution on YOUR website! The answer to this question depends on what is understood by word mistake and word in. If we are really talking about mistakes in lines, then there is only one line that contains an unusual symbol, which is meant to mean "greater than or equal to". The symbol for this expression using only ASCII text is normally written as ">=" and not as "=>". I could see how some people would say that this is a mistake although I personally would not use such a strong word.
If we are talking about the mistakes made in the solution process then we could have mistakes in the following logical transitions:
- from the original inequality to the statement made in line 1,
- from the statement made in line 1 to the statement made in line 2, and
- from the statement made in line 2 to the statement made in line 3.
Out of all of these, there is a mistake made in the logical transition from line 1 to line 2 only. All the other logical transitions are OK.
A fair but perhaps not very useful answer to this question would be this:
Except for an unusual ASCII representation of the "greater than or equal to" phrase, there are no mistakes in any of the lines. There is a mistake made in the transition process from line 1 to line 2 and there is a mistake in the way the question is asked.
A useful answer to this question would be:
B
(This is because it seems most likely that the one who asked the question is going to mark that answer as the correct one).
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