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 \boxedx - 1`