Solving problems does not have to be as confusing as some people make it. The biggest thing is to recognize when you have an expression versus an equation (or inequality). If all you have is an expression, the only thing you can do is change its form; that is, simplify, factor, perform a specific operation, and so on. It is only when you have an equation (or inequality) that you can solve for values that make the equation (or inequality) a true statement.
What I want to do here is collect in one place all of the strategies that we have studied for solving equations (or inequalities). For the most part, the strategies are the same whether it is an equation or an inequality. Some of the details might vary, such as what happens when one multiplies or divides by a negative quantity, but the strategies are generally the same. For brevity, I will refer only to equations in these notes.
To begin with, an equation is two expressions that have been set equal to each other. Equivalently, an equation is two expressions separated by an equal sign (=).