Question

Write the absolute value equation representing all numbers x whose distance from 4 is 8 units.?

Answer 1

`abs(x-8)=4`
`x= {-4, 12}`

Explanation:

We are told that `x` is the set of numbers such that the distance from `x` to `4` is `8` - We'll assume `x in RR`

The distance of `x`, positive or negative, from 4 can be expressed as `abs(x-4)`

Since this distance is equal to `8` our equation is:

`abs(x-4) =8`

To solve for `x`:

Either +(x-4) = 8 -> x=12#

Or -(x-4) = 8 -> x=-4#

Hence, set `x ={-4, 12}`