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14 May 2019, 22:36
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Hi,
So im a bit overwhelmed with the whole concept of inequalities. Just wanted to check with you the 4 main points that I have identified.Please correct me if I am wrong
1. Modulus
For equations like |x-a|=b . we take two conditions of x-a=b and x-a=-b and solve. WE DONT NEED TO PUT BACK THE SOLUTIONS TO CHECK EXTRANEOUS SOLUTIONS.
2. Modulus with variable on both side
For equations like |x-a|=x^2+b . We have to take two conditions and check if the solutions are extraneous by plugging in values and taking only LHS=RHS values
3. Inequalties and absolute value
For equations like -a<|x+a|<a Take the two cases. find the solutions using number line and then take the common solutions. If no common solution then we write the solutions as OR
4. Quadratic inequalities
Equate the equation to 0. Find the solutions and put the solutions in number line. Take 3 different areas and take sample values from each of them to check if the inequality is true.
Bunuel GMATPrepNow carcass
So im a bit overwhelmed with the whole concept of inequalities. Just wanted to check with you the 4 main points that I have identified.Please correct me if I am wrong
1. Modulus
For equations like |x-a|=b . we take two conditions of x-a=b and x-a=-b and solve. WE DONT NEED TO PUT BACK THE SOLUTIONS TO CHECK EXTRANEOUS SOLUTIONS.
2. Modulus with variable on both side
For equations like |x-a|=x^2+b . We have to take two conditions and check if the solutions are extraneous by plugging in values and taking only LHS=RHS values
3. Inequalties and absolute value
For equations like -a<|x+a|<a Take the two cases. find the solutions using number line and then take the common solutions. If no common solution then we write the solutions as OR
4. Quadratic inequalities
Equate the equation to 0. Find the solutions and put the solutions in number line. Take 3 different areas and take sample values from each of them to check if the inequality is true.
Bunuel GMATPrepNow carcass
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AlN
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14 May 2019, 22:45
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15 May 2019, 09:05
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For #1, yes, while that's not the absolute value method I would use, it will work for the simplest equations, like the one you mention. The lone exception would be for equations that have no solutions at all -- for example, if you had this equation
|x - 4| = -2
just unthinkingly solving it using cases will lead you to think there are two solutions, when there are none. Of course, you'd almost never see an equation like that in a GMAT question -- the only way you would is in a question that asks something like "which of the following equations has more than one solution for x", say.
For #2: yes, as soon as you start seeing more complicated absolute value equations, you'll run the risk of getting 'phantom solutions' if you just solve unthinkingly using cases. There are a few ways to avoid that problem; plugging your solutions back in to confirm they 'work' is one way (not the best way, in my opinion, because it is awkward to use when you have inequalities instead of equations, but it will definitely work just fine with equations). Complicated equations with absolute values in them are rare on the GMAT though, so while it's not impossible, it's very unlikely you'll need to worry about this issue on the test.
For #3: I don't follow precisely what you're saying, but I would never use cases in that situation regardless. I would interpret the absolute value as a distance on the number line instead - much easier and much less confusing (I can't explain that method fully here, but I have in posts a long time ago on this forum).
For #4: also not the method I would use, but the method you're suggesting will work. And it should be fine except on some 750+ level questions.
|x - 4| = -2
just unthinkingly solving it using cases will lead you to think there are two solutions, when there are none. Of course, you'd almost never see an equation like that in a GMAT question -- the only way you would is in a question that asks something like "which of the following equations has more than one solution for x", say.
For #2: yes, as soon as you start seeing more complicated absolute value equations, you'll run the risk of getting 'phantom solutions' if you just solve unthinkingly using cases. There are a few ways to avoid that problem; plugging your solutions back in to confirm they 'work' is one way (not the best way, in my opinion, because it is awkward to use when you have inequalities instead of equations, but it will definitely work just fine with equations). Complicated equations with absolute values in them are rare on the GMAT though, so while it's not impossible, it's very unlikely you'll need to worry about this issue on the test.
For #3: I don't follow precisely what you're saying, but I would never use cases in that situation regardless. I would interpret the absolute value as a distance on the number line instead - much easier and much less confusing (I can't explain that method fully here, but I have in posts a long time ago on this forum).
For #4: also not the method I would use, but the method you're suggesting will work. And it should be fine except on some 750+ level questions.
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!
