Question

|x-1| if x>1 how do you simplify this

Answer 1

Use the definition of absolute value.

$|x| = \begin{cases} x & \text{if } x \ge0 \\ -x & \text{if } x < 0 \end{cases}$

The absolute value is always non-negative. So if $x$ is already non-negative, $|x|=x$ is unchanged. But if $x$ is negative, then $|x|=-x$ because multiplying $x$ by -1 makes it positive.

Now, if $x>1$, then by the definition of absolute value,

$x > 1 \implies x - 1 > 0 \implies \boxed{|x - 1| = x - 1}$