Question

Which number line shows the solution set for |y-9| <12

Answer 1

its c the answer above me is correct

Explanation:

Answer 2

Option c

`y\geq-3` or
`y \leq 21`

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 inequation:

`|y-9| \leq 12` has two cases

`(y-9)` if
`y \geq 9` (i)

`-(y-9)` if
`y < 9` (ii)

We solve the case (i)

`y \leq 9 + 12\\y\leq21`

We solve the case (ii)

`-y +9 \leq 12\\-y \leq 12-9\\y \geq -3`

Then the solution is:

`y\geq-3` or
`y \leq 21`