So, I'm guessing $\displaystyle 2a+8=2a-6$ would have no solution. $\displaystyle 2a+8=-2a+6$ would come out to $\displaystyle a=-1/2$
Correct?
I was on the right track, just wasn't sure of myself.
Don't guess! If 2a+ 8= -2a+ 6, adding 2a to both sides gives 8= 6 which is NOT true. There is no value of a which makes it true. Yes, if a= -1/2,
then 2a+ 8= 2(-1/2)+ 8= -1+ 8= 7 and |7|= 7, while 2a- 6= 2(-1/2)- 6= -1- 6= -7 and |-7|= 7.