Please help?
What is the solution set of |x – 2| + 4 = 3?

Question

Please help?
What is the solution set of |x – 2| + 4 = 3?

jim_thompson5910 · Answer

subtract 4 from both sides to get

|x – 2| + 4 = 3

|x – 2| + 4-4 = 3-4

|x – 2| = -1

do you see what to do from here?

jim_thompson5910 · Answer

keep in mind that |x| is either 0 or some positive number since the absolute value represents distance

so |x-2| is either 0 or some positive number

anonymous · Answer

I don't know what to do next? Do I add 2 to both sides?

jamesj · Answer

Well, since |x-2| must be zero or positive, for what values of x is it the case that
|x-2| = -1 ?

jim_thompson5910 · Answer

|x-2| = -1 is basically saying "x is some number on the number line that is -1 units away from 2"

is that possible?

anonymous · Answer

No

anonymous · Answer

$|x-2|=-1$ stipulates $x-2=-1$ and $2-x=-1$.

jim_thompson5910 · Answer

since it's not possible, there are no solutions

anonymous · Answer

Whoops, that's right, no possible solutions. Durr.

anonymous · Answer

Oh! I see now. No wonder it didn't make sense... Ha ha thanks, guys!