Question

Write each of the following expressions without using absolute value. |7m–56|, if m<8

Answer 1

`|7\cdot m -56| = -7\cdot m + 56` if
`m< 8`

Explanation:

According to the definition of absolute value:

`f(x)` if
`f(x) \geq 0`

`-f(x)` if
`f(x) <0`

If
`m < 8`, then:

`y_(max) = 7\cdot (8) - 56`

`y_(max) = 0`

`y` becomes negative as
`m` diverges to
`-\infty`.

Then, the absolute value can be rewritten as follows:

`|7\cdot m - 56| = -(7\cdot m -56)` if
`m <8`

`|7\cdot m -56| = -7\cdot m + 56` if
`m< 8`