permit me to ask this somewhat dumb question:
how do i translate a number line inequality to an expression in absolute form?
For example, how to convert the attached number line diagram diagram to its absolute form:
Inequality: -3 <= x < 7
Absolute form: ???
Thanks.
converting Inequality to absolute form
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- shashank.ism
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absolute form ... Hmmm.... ok Go this way..
First look at the endpoints. Negative -3 and 7 are 10 units apart. Half of 10 is 5. So I want to adjust this inequality so that it relates to -5 and 5, instead of to -3 and 7. To accomplish this, I will adjust the ends by subtracting 2 from all both sides
-3 <= x <= 7
-3 - 2 <= x - 2 <= 7-2
-5 <= x - 2 <= 5
--> |x-2| <=5
There it is you got your answer... cheers
First look at the endpoints. Negative -3 and 7 are 10 units apart. Half of 10 is 5. So I want to adjust this inequality so that it relates to -5 and 5, instead of to -3 and 7. To accomplish this, I will adjust the ends by subtracting 2 from all both sides
-3 <= x <= 7
-3 - 2 <= x - 2 <= 7-2
-5 <= x - 2 <= 5
--> |x-2| <=5
There it is you got your answer... cheers
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- krusta80
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So, to generalize, for all inequalities with a < 0 and b > 0:gmatdriller wrote:permit me to ask this somewhat dumb question:
how do i translate a number line inequality to an expression in absolute form?
For example, how to convert the attached number line diagram diagram to its absolute form:
Inequality: -3 <= x < 7
Absolute form: ???
Thanks.
a < x < b
We can convert to |x - (b+a)/2| < (b-a)/2, when |a| <= |b|
and |x + (b+a)/2| < (b-a)/2, when |a| > |b|
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Thanks for the posts.
for one, i can convert single segment inequality to its absolute form.
I could not do same for two segment inequalities (that is quadratic forms).
this is similar to the OR (|x-a| > b) situation
Is this knowledge necessary for the gmat test?
for one, i can convert single segment inequality to its absolute form.
I could not do same for two segment inequalities (that is quadratic forms).
this is similar to the OR (|x-a| > b) situation
Is this knowledge necessary for the gmat test?
- shashank.ism
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krusta80 wrote:So, to generalize, for all inequalities with a < 0 and b > 0:gmatdriller wrote:permit me to ask this somewhat dumb question:
how do i translate a number line inequality to an expression in absolute form?
For example, how to convert the attached number line diagram diagram to its absolute form:
Inequality: -3 <= x < 7
Absolute form: ???
Thanks.
a < x < b
We can convert to |x - (b+a)/2| < (b-a)/2, when |a| <= |b|
and |x + (b+a)/2| < (b-a)/2, when |a| > |b|
Yes you are correct krusta... anyway we don't need any generalization... just check problem and solve it in seconds....
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- shashank.ism
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Yup there is a Thanks button for that ....gmatdriller wrote:Thanks for the posts.
for one, i can convert single segment inequality to its absolute form.
I could not do same for two segment inequalities (that is quadratic forms).
this is similar to the OR (|x-a| > b) situation
Is this knowledge necessary for the gmat test?
In quadratic form u get 2 soultions. and there is an OR so if it gets continous result.... u can do it.. like x<3 or x>24
otherwise not
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