Question

Which number line shows the solution set for |h-2| = 4

Answer 1

`h = -2\\h = 6`

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:

`|h-2| = 4` has two cases

`(h-2) = 4` if
`h > 2` (i)

`-(h-2) = 4` if
`h < 2` (ii)

We solve the case (i)

`h = 4 + 2\\h = 6`

We solve the case (ii)

`-h +2 = 4\\h = 2-4\\h = -2`

Then the solution is:

`h = -2` or
`h = 6`

Answer 2

The Second Option is your Answer ( Option 2)

Explanation:

1) proof ( replace h with -2)

|-2-2| = 4

|-4| = 4

2) proof ( replace h with 6)

|6-2| = 4

|4|=4

Hopes this helps !