I have a question on negative numbers in absolute value equations.

For instance:

This is fine for me. I'm assuming that the result is a negative based on the division by -3. The book says that's correct.

The other solution is what's giving me trouble. I get -7 and the book says 7.

Am I supposed to think that is the same as a negative divided by a negative? That would work out to a positive. If that's true then would be 2.33 in decimal. I'm going to convert it to a graphing equation and check out the vectors but I really would like to hear an explanation of the negative number thing in absolute value equations. I'm thinking that because -3x is an absolute value that it's either positive or negative and so when I can simplify to a whole number it's a positive, and then again, maybe not.

Thanks! Hope you are having a great weekend!