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almond37 [142]
1 year ago
10

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

Mathematics
1 answer:
JulsSmile [24]1 year ago
4 0

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}

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