Question

How do you solve `16= | 3m - 4| - 11`?

Answer 1

`-23/3` and `31/3`

Explanation:

`16 = abs(3m - 4) - 11`

`27 = abs(3m - 4`

Some people teach that "absolute value" means the number is positive, but that's not entirely accurate. Absolute value tells us how far the number is from 0 when we put it on the number line. There is no such thing as `- 14` feet or `- 8` meters.
So, a negative number or a positive number will yield the same value: `abs(-8) = abs(8) = 8`

So, we have two values to solve for

`27 = 3m - 4` and `-27 = 3m - 4`

`* * * * * * * * * * *`

`27 = 3m - 4`

`31 = 3m`

`m = 31/3`

`* * * * * * * * * * *`

`-27 = 3m - 4`

`-23 = 3m`

`m = -23/3`

So, we have two answers! And to check our work, let's graph the equation and see the `x`- intercepts

graph{y=abs(3x - 4)-27}

`-7.667` and `10.333`, which are the decimal approximations for

`-23/3` and `31/3`.

We were right! Nice work!