Answer:
Option A is correct.
Values of x :
x = 0 and x =4
Step-by-step explanation:
Absolute function states that contains an algebraic expression within absolute value symbols i,e
[tex]|x| = \left\{\begin{matrix}x & if x>0 \\ 0 & if x = 0\\ -x & if x< 0 \end{matrix}\right.[/tex]
Given that: [tex]|x-2|+10=12[/tex] .....[1]
solve for x;
Subtract 10 from both sides in equation [1] we get;
[tex]|x-2|+10-10=12-10[/tex]
Simplify:
[tex]|x-2|=2[/tex]
By definition of Absolute;
(x-2) = 2 and -(x-2) = 2
or
x-2 =2 and x -2 = -2
we have;
x = 2+2 and x= -2+2
x = 4 and x = 0
Therefore, the value of x are 4 and 0.
