Question

How do you solve and graph `4<y+2<-3(y-2)+24`?

Answer 1

`2 < y < 7`
`color(white)("XXXX")`(see below for number line graph)

Explanation:

Treat the two inequalities separately then recombine.

Inequality 1: `color(white)("XXXX")` `4 < y + 2`
Subtracting `2` from both sides gives:
`color(white)("XXXX")` `2 < y`

Inequality 2: `color(white)("XXXX")` `y + 2 < -3(y - 2) +24`
Simplifying the `-3(y-2)` term:
`color(white)("XXXX")` `y + 2 < -3y +6 + 24`
Basic arithmetic
`color(white)("XXXX")` `y + 2 < -3y +30`
Add `(3y-2)` to both sides
`color(white)("XXXX")` `4y < 28`
Divide both sides by `4`
`color(white)("XXXX")` `y < 7`

Recombining
`color(white)("XXXX")` `2 < y < 7`