Question

How do you solve `abs(y+3)+4=20`?

Answer 1

`y=-19" or " y=13`

Explanation:

`"Isolate " |y+3|" by subtracting 4 from both sides"`

`|y+3|cancel(+4)cancel(-4)=20-4`

`rArr|y+3|=16`

`"the expression inside the absolute value can be positive or"`
`"negative"`

`rArry+3=16toy=16-3=13larr(color(red)(1))" or "`

`-(y+3)=16`

`rArr-y-3=16to-y=16+3toy=-19larr(color(red)(2))`

`color(blue)"As a check"`

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

`y=13to|13+3|+4=|16|+4=16+4=20`

`y=-19to|-19+3|+4=|-16|+4=20`

`rArry=-19" or " y=13" are the solutions"`