Thank you @Carcass, I'll follow the rules next time

Hi thanks for your reply. Just one confusion about flipping of sign here.
0.1x - 3 >= -1
0.1x >= -1+3
0.1x >= 2

why the sign will flip when there is no negative sign?

Think of "Absolute value" as "distance away from zero on a number line". No matter whether you're going in a positive or a negative direction, the actual distance is always going to be positive (asan analogy, think about going 50 miles east or 50 miles west on a map---no matter which direction you go, you've still gone 50 miles.)

The inequality \(|0.1x-3|>=1\) tells you that whatever is inside the absolute value sign "||" is 1 or more units away from zero. We can see that that's obviously true for numbers like 1,2,2.5,3, etc....but it's also true for -1, -2, -2.5, -3, etc.

So whenever you have an absolute value inequality, you'll typically need to set up two equations, one for the positive direction, and one for the negative. Then solve each separately, to find the range of possible values.

You mean to say whenever we set up the equation for negative value we have to flip the sign from start? and no need to wait for the answer i.e if answer is negative only then flip the sign?

The purpose of the two equations (or inequalities) is to solve for the values both above your starting point (i.e. in a positive direction) and below (in a negative direction).

Say you had something like
|x| > 3

This is really saying that "the distance away from zero is greater than 3 units.

So the first equation would simply be x > 3.

But the numbers less than -3 are ALSO more than 3 units away from zero, just in the opposite direction.

In other words, it's also true that x < -3.

So, for inequalities with absolute values, you'll have two equations:

Equation #1 -- simply remove the || sign.
Equation #2-- make the right side negative, and flip the sign.

Here's an example:

|x+2| > 4

First Equation (simply remove the || sign):
x+2 > 4

Second Equation:
x+2 < -4

Thank you very much for your help. It was a very important point. I used to get confused a lot in inequalities. Hope I'll do better now

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.