Question

How do you solve `6|y+1|=60`?

Answer 1

See the entire solution process below.

Explanation:

First, divide each side of the equation by `color(red)(6)` to isolate the absolute value term:

`(6abs(y + 1))/color(red)(6) = 60/color(red)(6)`

`(color(red)(cancel(color(black)(6)))abs(y + 1))/cancel(color(red)(6)) = 10`

`abs(y + 1) = 10`

The absolute value function transforms any negative or positive term into its positive form. Therefore, to solve this you need to solve the term within the absolute value function for both the negative and positive form of what it is equated to.

Solution 1)

`y + 1 = -10`

`y + 1 - color(red)(1) = -10 - color(red)(1)`

`y + 0 = -11`

`y = -11`

Solution 2)

`y + 1 = 10`

`y + 1 - color(red)(1) = 10 - color(red)(1)`

`y + 0 = 9`

`y = 9`

The solution is `y = -11` and `y = 9`