When we plug 6 and -4 in for x, we end
up with the absolute value of 8 which is 8. When we plug 4 and -2
in for x, we end up with the absolute value
of -8 which is also 8.
If you would have only come up with an answer of x = 6 and -4, you would not have gotten all solutions to this problem.
Again, it is important to note that we are using the definition of absolute
value to set the two equations up. Once you apply the definition
and set it up without the absolute value, you just solve the quadratic equation
as shown in Tutorial 17: Quadratic
Equations.
There are four solutions to this absolute value equation: 6, -4,
4, and -2. |