Question

How do you solve `abs(4y+5)=7`?

Answer 1

`y = 1/2` and `y = -3`

Explanation:

Because the absolute value function transform positive or negative number into a positive number we need to solve the interior of the absolute value function for both the negative and positive form of its equality:

Solution 1)

`4y + 5 = color(blue)(7)`

`4y + 5 - color(red)(5) = 7 - color(red)(5)`

`4y + 0 = 2`

`4y = 2`

`(4y)/color(red)(4) = 2/color(red)(4)`

`(color(red)(cancel(color(black)(4)))y)/color(red)(cancel(color(black)(4))) = 1/2`

`y = 1/2`

Solution 2)

`4y + 5 = color(blue)(-7)`

`4y + 5 - color(red)(5) = -7 - color(red)(5)`

`4y + 0 = -12`

`4y = -12`

`(4y)/color(red)(4) = -12/color(red)(4)`

`(color(red)(cancel(color(black)(4)))y)/color(red)(cancel(color(black)(4))) = -3`

`y = -3`