Question

|x-y| if x < y


Help Pls!!!

Answer 1

y -x

Explanation:

You want to know the value of |x -y| when x < y.

Absolute value

The absolute value function is defined piecewise:

`|x|=\begin{cases}-x,&\text{for }x < 0\\x,&\text{for }x\ge0\end{cases}`

Application

When this is applied to the given expression, it becomes ...

`|x-y|=\begin{cases}y-x,&\text{for }x < y\\x-y,&\text{for }x\ge y\end{cases}`

Since we're concerned only with the case x < y, the value is ...

|x -y| = y -x . . . . . when x < y

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Answer 2

Answer and Explanation:

The absolute value expression:

| x - y |

yields the positive difference between the numbers x and y.

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The absolute value function is defined as:

`| \, x\, | = \begin{cases}x \ \ \, \text{ if } x > 0 \\ -x \text{ if } x < 0\end{cases}`

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To write a statement that is equal to the given one but without the absolute value, we have to use the information that:

• y is greater than x

and therefore it must be the number being subtracted from:

• y - x