Question

How do you solve the inequality: `0 < 2y + 8 < 12`?

Answer 1

`-4 < y < 2`

Explanation:

Things you can do to both sides of an inequality while maintaining the validity of the inequality:

• Add or subtract any amount to/from both sides
• Multiply or divide by any amount greater than zero

While it is possible to solve a compound expression (with more than one inequality symbol) it is probably safer to handle the two pieces separately and then recombine.

`0 < 2y + 8 < 12`
will be treated as
Part 1: `0 < 2y + 8` and
Part 2: `2y + 8 < 12`

Part 1
`0 < 2y +8`
`rarr` `color(white)("XXXX")` `-8 < 2y`
`rarr` `color(white)("XXXX")` `-4 < y`

Part 2
`2y + 8 < 12`
`rarr` `color(white)("XXXX")` `2y < 4`
`rarr` `color(white)("XXXX")` `y < 2`

Recombining
`color(white)("XXXX")` `-4 < y < 2`