posted by lindsay on .
Calculat the absolute value of:
PS. The brackets are supposed to be the straight lines for the absolute symbols.
who are all these people that can't find the "|" key? It's shift-\ on every keyboard I've seen.
4-|x-3| = 0
if (x-3) > 0, |x-3| = x-3 and we have
4-(x-3) = 0
4-x+3 = 0
7-x = 0
x = 7
if (x-3) < 0, |x-3| = -(x-3) = 3-x
4-(3-x) = 0
1+x = 0
x = -1
Note that sometimes there are unusable solutions, as in some case where you have
if (x+3) > 5
and you end up with a "solution" of x = -2
which does not satisfy the condition.
In this problems, the solutions obeyed the conditions.
In order to void the absolute value bars, it needs to stand by itself.
Now get rid of the value bars and you get:
7 = x
Plug it in and see !