Question

How do you evaluate `5x-|y-x|` when `x=-3, y=6`, and `z=-7`?

Answer 1

See a solution process below:

Explanation:

First substitute `color(red)(-3)` for `color(red)(x)` and `color(blue)(6)` for `color(blue)(y)`:

`5color(red)(x) - abs(color(blue)(y) - color(red)(x))` becomes:

`(5 xx color(red)(-3)) - abs(color(blue)(6) - color(red)(-3))`

Remembering "minus a minus is a plus" allows us to rewrite the expression as::

`(5 xx color(red)(-3)) - abs(color(blue)(6) + color(red)(3))`

Next we can execute the operations in the parenthesis and within the absolute value function:

`-15 - abs(9)`

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

This gives us:

`-15 - 9 => -24`