Question

How do you solve `y=abs(2x+3)`?

Answer 1

Assuming that all you require to "solve" this equation is to state it without the absolute value operation:

If `2x+3<0`
`rarr x<-3/2`
then
`y=abs(2x+3)`
`rarr y=-2x-3`

If `2x+3>=0`
`rarr x>= -3/2`
then
`y=abs(2x+3)`
`rarr y = 2x+3`

Therefore
`y=abs(2x+3){(-= y=-2x-3 " if " x<-3/2),(-=y=2x+3 " if " x>= -3/2):}`