Absolute value of y

[akash.a.pradhan]

Hi,

I wanted to see if someone could help provide the algebraic solution to the following problem:

y^3 is less than or equal to absolute value of y

If y is positive, I understand how you algebraically solve to get the upper bound of y=1. However, how do you algebraically solve for the y is negative case? I wasn't algebraically able to arrive at the correct answer (y<0) on that side.

Thanks!

[rihanna.hayat]

Hi,

I wanted to see if someone could help provide the algebraic solution to the following problem:

y^3 is less than or equal to absolute value of y

If y is positive, I understand how you algebraically solve to get the upper bound of y=1. However, how do you algebraically solve for the y is negative case? I wasn't algebraically able to arrive at the correct answer (y<0) on that side.

Thanks!

Hi,
I cannot understand what you mean by "If y is positive, I understand how you algebraically solve to get the upper bound of y=1."
This is my interpretation:
Given condition: y^3 is less than or equal to lyl
1. If y>0,
y can be a proper fraction , in case y^3 is less than lyl
OR
y can be 1, in case y^3 is equal to lyl

2.If y<0, then y^3 will always be less than lyl because
if y<0 then y^3 <0 and
lyl > 0 always.

[RonPurewal]

Hi,

I wanted to see if someone could help provide the algebraic solution to the following problem:

y^3 is less than or equal to absolute value of y

If y is positive, I understand how you algebraically solve to get the upper bound of y=1. However, how do you algebraically solve for the y is negative case? I wasn't algebraically able to arrive at the correct answer (y<0) on that side.

Thanks!

If y is negative, then there's no sense in trying to solve algebraically -- just think about signs!
If y < 0, then y^3 is also negative, but |y| is positive. Therefore, the inequality is true for all negative numbers.

If you insist on solving algebraically (hopefully to learn some lessons for future problems, since there's no point in doing so here), then you can just replace |y| with (-y), because |y| is equal to -y for all negative y's.
then you have y^3 < -y, which you would solve as you would any other inequality of that sort (ignoring any positive solutions, of course).