Calculat the absolute value of:
4-{x-3}=0
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.
So 4=|x-3|
Now get rid of the value bars and you get:
7 = x
Plug it in and see !
To find the absolute value of an expression, you need to isolate the expression inside the absolute value symbols and evaluate it. Let's solve the equation step by step:
Step 1: Rewrite the equation with the absolute value symbol:
|4 - (x-3)| = 0
Step 2: Simplify the expression inside the absolute value:
|4 - x + 3| = 0
Step 3: Combine like terms:
|7 - x| = 0
Step 4: Since the absolute value of any number, except 0, is always positive, the only way the absolute value of an expression can be equal to 0 is when the expression inside the absolute value is also equal to 0.
So, set 7 - x = 0 and solve for x:
7 - x = 0
-x = -7
x = 7
Therefore, the absolute value of 4 - (x-3) equals 0 when x = 7.