Use the definition of absolute value.
[tex]|x| = \begin{cases} x & \text{if } x \ge0 \\ -x & \text{if } x < 0 \end{cases}[/tex]
The absolute value is always non-negative. So if [tex]x[/tex] is already non-negative, [tex]|x|=x[/tex] is unchanged. But if [tex]x[/tex] is negative, then [tex]|x|=-x[/tex] because multiplying [tex]x[/tex] by -1 makes it positive.
Now, if [tex]x>1[/tex], then by the definition of absolute value,
[tex]x > 1 \implies x - 1 > 0 \implies \boxed{|x - 1| = x - 1}[/tex]
