help with math!?!?

Question

how do you solve !x-3! the ! are absolute value signs..sorry. idk how to type it.

also how would you graph such an inequality? thanks for all the help.

Answer 1

If the absolute value of some quantity |x| is less than some other quantity, i.e. |x| < y, this means the same as:

-y < x < y

So for your question, you have

-x < x -3 < x
subtract everything by x

-2x < -3 < 0

We know that -3 is less than 0, so all we have is:

-2x < -3, or otherwise, x > 3/2 (divide both sides by -2, then you have to flip the equality sign).

That's actually a tricky question. Forget about the person above this one.

Answer 2

You don't have the pipe character on your keyboard, above the enter key? That's weird. Anyway...

|x-3| is always non-negative, so it can mean x-3 if x-3 is positive, or it could be -(x-3) if it's negative (if x=3 this means x-3 = 0 and it doesn't matter either way). In the case of x-3 < x, this means -3 < 0. This is always true. So look at the second case.
-(x-3) < x
x-3 > -x
2x > 3
x > 3/2

So the original inequality simplifies to x > 3/2.

Answer 3

Use shift backstroke to type |x-3|.