The given expression is [tex]|2 x-2|=x+1[/tex]
We need to determine the solution to the expression.
Solution:
The absolute value of the expression [tex]|2 x-2|=x+1[/tex] is given by
[tex]2 x-2=x+1[/tex] or [tex]2 x-2=-(x+1)[/tex]
Let us solve the expression [tex]2 x-2=x+1[/tex]
Thus, we get;
[tex]x-2=1[/tex]
[tex]x=3[/tex]
Now, solving the expression [tex]2 x-2=-(x+1)[/tex]
Thus, we get;
[tex]2x-2=-x-1[/tex]
[tex]3x-2=-1[/tex]
[tex]3x=1[/tex]
[tex]x=\frac{1}{3}[/tex]
Thus, the solution of the expression is [tex]x=3[/tex], [tex]x=\frac{1}{3}[/tex]
Hence, Option B is the correct answer.
