Why Don't They Understand?!?

So one of the things I've been most frustrated by in recent weeks is that my students who are in an Algebra II class don't seem to understand the basics of algebra. Most of my students failed the last quiz, and I was really upset by that. But upon further investigation of their quizzes, I realized that most of them were failing not because they didn't understand the concepts of substitution and elimination but because they didn't now how to manipulate equations. Most of them did not understand why you have to do the same operation to both sides of the equation. It was such a depressing moment for me, because I realized that I don't even know how to proceed with this course if they don't understand things they should have mastered at least a year ago. It would be different if it were only 5-7 students in my class in this position, but it appears to be at least half of them. I think I'm going to require that a group of students come to a review session after school this week because they will never progress or pass the MCAS without understanding algebraic manipulation. It's very good that I chose to do my semester project for my math/science teaching class on the concept of the equals sign. I hope it sheds some light on the matter for when I teach this in the future.