Question

Which number line shows the solution set for |p-3| = 9

Answer 1

Second Option

`p = -6` and
`p = 12`

Explanation:

The absolute value is a function that transforms any value x into a positive number.

Therefore, for the function
`f(x) = |x|` x> 0 for all real numbers.

Then the equation:

`|p-3| = 9` has two cases

`(p-3) = 9` if
`h > 3` (i)

`-(p-3) = 9` if
`h < 3` (ii)

We solve the case (i)

`p = 9 + 3\\p = 12`

We solve the case (ii)

`-p +3 = 9\\p = 3-9\\p = -6`

Then the solution is:

`p = -6` or
`p = 12`