Question

How do you graph and solve `|4y+3| -8<= -3`?

Answer 1

`-2<=y<=1/2`

Explanation:

Rearranging the equation
`∣4y+3∣<=8-3<=5`
So we have to solve
`∣4y+3∣<=5`
The solutions are
`4y+3<=5` and `-(4y+3)<=5`
So we have to solve
`4y<=2` and `-4y-3<=5`
`y<=1/2` and `4y>=-8` =>`y>=-2`
So the solutions are `-2<=y<=1/2`
Checking, if y=0
LHS =`3-8=-5`
RHS =`-3`
so `LHS<=RHS`