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05 Jun 2019, 00:18
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While solving absolute inequality questions, I have gone through 1 question and found the following solution.
The question was
What is the solution of the following equation 7 > |-3a + 5|,
Solution was
i.
7 > +(-3a+ 5)
2 > -3a
2/3>-a
a>-2/3
and
ii.
7 > -(-3a + 5)
7 > 3a
12 > 3a
4 > a
so the solution is
-2/3<a<4
If the above-mentioned solution is correct, then it is diluting the meaning of the absolute value of "-3a + 5". Why we are considering both +ve and -Ve values of -3a + 5, when only abolute value is less than 7. The negative value of "-3a + 5" may not be lesser than 7. Then how can we consider negative value as one of the solutions.
If anybody can explain the logic behind this, please comment.
The question was
What is the solution of the following equation 7 > |-3a + 5|,
Solution was
i.
7 > +(-3a+ 5)
2 > -3a
2/3>-a
a>-2/3
and
ii.
7 > -(-3a + 5)
7 > 3a
12 > 3a
4 > a
so the solution is
-2/3<a<4
If the above-mentioned solution is correct, then it is diluting the meaning of the absolute value of "-3a + 5". Why we are considering both +ve and -Ve values of -3a + 5, when only abolute value is less than 7. The negative value of "-3a + 5" may not be lesser than 7. Then how can we consider negative value as one of the solutions.
If anybody can explain the logic behind this, please comment.
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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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10 Jun 2019, 14:06
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tamalmallick
First of all, the solution is correct. A good way to double check that it's correct is to plug in some values for a. The solution says that a is between -2/3 and 4; try the extreme values:
|-3(-2/3) + 5| = |2 + 5| = |7| = 7, so if a is a tiny bit greater than -2/3 (closer to 0), the absolute value will be less than 7.
|-3(4) + 5| = |-12 + 5| = |-7| = 7; likewise.
Also, try at least one value in the middle:
|-3(0) + 5| = |5| = 5, which is less than 7.
It seems like the answer is right.
I'm not totally sure I understand your question, but I think your concern has something to do with the idea of the 'negative value' of -3a + 5. Be aware that the 'negative value' of this expression isn't necessarily a negative number. For example, if a = 3, then the 'negative value' is -(-3a + 5) = -(-4) = 4. Think of the negative sign as being a 'reverse the sign' marker, not a marker saying that the expression has to be negative.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
