Which of the following number line graphs shows the solution set to this inequality?

[abplesauc]

I tried to add 5 to both sides to get... x<4.

But that isn't correct because x = 3 doesn't work; it's untrue that 2<-1.

Does this not work because it's an inequality? Although, I don't get why it wouldn't work.

To find the solution, it seems like you just have to use trial and error. Is that the only method of finding the solution?

 

[mmm4444bot]

Absolute value is never negative.

In other words, the expression |x - 5| cannot represent any value that is less than zero.

Can you pick the correct answer now? :cool:

 

[crybloodwing]

So absolute value is the distance of an expression/function from 0.

Think of it as riding a bike. You can ride 5 feet forwards. Even if you start again and ride 5 feet in the other direction, you still rode 5 feet, not -5 feet.

So, absolute value is always 0 or greater. It can not be negative.

Therefore, |x|>0 exists and |x|<0 can not exist. Replace x with (x-5).

So |x-5|<0. Is -1 less than 0? Yes. This can not exist.

 

[stapel]

The original exercise is:

Which of the following is the solution set to \(\displaystyle \Big\lvert\, x\, -\, 5\, \Big\rvert \, < \, -1\)?

F. the interval (4, 6)
G. the interval (-infinity, 4)
H. the interval (6, +infinity)
J. the intervals (-infinity, 4) and (6, +infinity)
K. the empty set

I tried to add 5 to both sides to get... x<4.

This would have resulted in the following new inequality:

. . . . .\(\displaystyle \Big\lvert\, x\, -\, 5\, \Big\rvert \, +\, 5\, <\, 4\)

How did you get from this to "x < 4"?

But that isn't correct because x = 3 doesn't work; it's untrue that 2<-1.

Does this not work because it's an inequality?

What is the "this" that "does...not work"?

To find the solution, it seems like you just have to use trial and error. Is that the only method of finding the solution?

No; whatever method they explained in the textbook should work. For further explanation of how to solve absolute-value inequalities, try here. (If you're not familiar with how to solve absolute-value equations, you might want to start with lessons on that first.)

Please study at least two lessons from the list. Once you've learned the basic terms and techniques, please return to this exercise. You'll then understand why the first step has to be the removal of the absolute-value bars. Only then does adding things to either side (well, all three sides, at that point) do any good.