Question

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

Answer 1

`|7m- 56| = 56 - 7m`

Explanation:

Given

`|7m- 56|`

`m < 8`

Required

Rewrite the expression without absolute values

The first step is to check if the expression in |...| is positive or negative;

The question says m < 8,

This means the value of m could be 7, 6 ...

Let's assume m is 7

`7m - 56 = 7 * 7 - 56 = 49 - 56 = -7`

This means that the expression
`|7m- 56|` will give a negative value if
`m < 8`

So,

`|7m- 56| = -(7m - 56)`

Open bracket

`|7m- 56| = -7m + 56`

Rearrange

`|7m- 56| = 56 - 7m`

The expression can't be further simplified