Solve |3x + 9| = 15.

An equation with absolute values in it will have two answers. We'll have the happy-go-lucky positive answer, and the sourpuss negative answer.

The first answer comes from keeping the inside of the absolute value the same, and solving.

3x + 9 = 15

3x = 6

x = 2

The second answer comes from finding the negative of what's inside the bars.

-(3x + 9) = 15

Let's multiply out the negative by -1, instead of distributing it.

3x + 9 = -15

3x = -24

x = -8

Our final answer is x = -8 or 2.

Solve 

One equation enters, two answers leave. The first just walks right out of its cage.

How about we divide the 2 out of our fraction, and then multiply each side by 9 after that? That sounds better than the alternatives, one of which involves 6 rubber chickens, a copy of Battlefield Earth, and the longest Friday night of our life.

x = 81

The second answer needs to put on a clever disguise to get out. A mop, some rags lying around, and a thick accent come together for a getaway that would make Scooby Doo and Shaggy proud.

x = -90

Our answer is x = 81 or -90. Shmoopy-doopy doo!

Solve |11 – 3x| = 13.

Can we rock this question to find the answers? Absolutely.

11 – 3x = 13

-3x = 2

One down, one to go.

-(11 – 3x) = 13

This time, we will distribute the -1, so that we can get rid of our negative coefficient on x.

-11 + 3x = 13

3x = 24

x = 8

The solutions to the equation are  or x = 8.