Nonlinear equations in one variable and systems of equations in two variables SAT question

The correct answer is $28$. The given absolute value equation can be rewritten as two linear equations: $4x-4=112$ and $-(4x-4)=112$, or $4x-4=-112$. Adding $4$ to both sides of the equation $4x-4=112$ results in $4x=116$. Dividing both sides of this equation by $4$ results in $x=29$. Adding $4$ to both sides of the equation $4x-4=-112$ results in $4x=-108$. Dividing both sides of this equation by $4$ results in $x=-27$. Therefore, the two values of $x-1$ are $29-1$, or $28$, and $-27-1$, or $-28$. Thus, the positive value of $x-1$ is $28$.

Alternate approach: The given equation can be rewritten as $|4(x-1)|=112$, which is equivalent to $4|x-1|=112$. Dividing both sides of this equation by $4$ yields $|x-1|=28$. This equation can be rewritten as two linear equations: $x-1=28$ and $-(x-1)=28$, or $x-1=-28$. Therefore, the positive value of $x-1$ is $28$.