Question

when you are solving an equation involving absolute values, do you have to have both negative and positve solutions??

not necessarily, it depends on the equation.

e.g.#1
│2x-1│ = 5

then (2x-)=5 or -(2x-1)=5
x=3 or x=-2

here you have a positive as well as a negative solution.

e.g.#2

│11-2x│ = 5

(11-2x) = 5 or -(11-2x) = 5
x=3 or x=8

both solutions are positive.