Question

Please help ASAP!!
What is the solution set of |x – 2| > 3?

Answer 1

x + 2 > 3
x > 1
All numbers greater than 1 would be in the solution set.

Answer 2

faulty......

2 is greater than 1
but 2 is most emphatically not in the solution set

Answer 3

@zugzwang, that's what I was going to say! It doesn't work..

Answer 4

The error was when it was (inaccurately) assumed that
|x - 2| = x + 2

So back to the inequality
|x - 2| > 3
Well, what if we just remove the absolute value?
x - 2 > 3

Answer 5

Would I have to solve for x - 2 > 3 and also x - 2 < 3?

Answer 6

It may be easier to see it without the the translation first....

What do you get if I give you
|y| > 3
?

Answer 7

y > 3, and also y < -3 right?

Answer 8

Correct. Now just replace y with x - 2, and you have what you need :)

Answer 9

So x > 5, and x < -1? :)

Answer 10

You got it :)

Answer 11

You can try it too, check those that are smaller than -1
and also check those larger than 5
You'll see it works every time

Answer 12

Thanks!