What does it mean to “Solve for x” or “Solve the Equation”?

Probably half of all of the directions in any algebra book say something along the lines of “solve the following for x”. We go through the steps we see in the examples and then move on right? But what are you really being asked to do?

Solve for x means find the value of x that would make the equation you see true.

Think about this equation: x + 1 = 3. If you were asked to solve it, that would mean finding some value for x that gives you three when you add one to it. Something plus one is three – what is the something? Well it must be two right? Since 2 + 1 = 3, x = 2. That’s it. That’s what solving an equation is all about!

This works no matter how complicated the equation gets. The only difference is that with a simple equation like this, it was possible to just think about it and get the answer. The more complicated the equation gets, well, there will be some more work involved. Either way – the idea is the same: Find the x that makes it true.

By the way, this is one of the great things about algebra – you can ALWAYS check your answers!