Answer
$x=-3\text{ or }x=5$.
Work Step by Step
Taking the negative value:
$$2(x-1)=-8$$
$$2x-2=-8$$
$$2x=-6$$
$$x=-3$$
Checking:
$$|2(-3-1)|=8$$
$$8=8~\checkmark \text{True}$$
Taking the positive value:
$$2(x-1)=8$$
$$2x-2=8$$
$$2x=10$$
$$x=5$$
Checking:
$$|2(5-1)|=8$$
$$8=8~\checkmark \text{True}$$
Thus, the solution is $x=-3\text{ or }x=5$.
