converting Inequality to absolute form

[gmatdriller]

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.

[shashank.ism]

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

[krusta80]

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.

So, to generalize, for all inequalities with a < 0 and b > 0:

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|

[gmatdriller]

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?

[shashank.ism]

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.

So, to generalize, for all inequalities with a < 0 and b > 0:

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....

[shashank.ism]

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?

Yup there is a Thanks button for that ....

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