I've to solve the following absolute value equation: |x - 3| - 4 = 0.
I found one of the answers which is 7 i.e.
|x - 3| - 4 = 0
x - 7 = 0
x = 7
However, my textbook also includes -1 as the answer. How did they get this answer?
Oh, ok! Got it now! thanks a lot!!
Does this mean we have to only do the following?
-(x - 3)-4 =0
-x + 3 - 4 = 0
-x + 3 = 4
x = -1
Is this the right way to solve?
To find the solution to the absolute value equation |x - 3| - 4 = 0, let's break it down into two separate equations:
1. x - 3 = 4
2. -(x - 3) = 4
1. In equation (1), solving for x will give you x = 7. This solution is correct, as you calculated.
2. In equation (2), we have the negative of the expression inside the absolute value brackets. Simplifying equation (2), we get -x + 3 = 4. Solving for x will give you x = -1.
Hence, the absolute value equation |x - 3| - 4 = 0 has two solutions: x = 7 and x = -1.
-x+3-4=0
-x+3=4
-x=1
x=-1