How to Solve Algebraic Equations

Video Transcript

"How do you solve algebraic equations? That sounds kind of tough. I'm Jimmy, and I'm here to show you an example as to how you would solve an algebraic equation. The first step is to exactly just read the directions carefully and see what it is they're asking for. You have an equation: 3x plus 14y is equal to two. Now, unfortunately, you're not going to know what to do if you don't read the directions. So just got to see what they're looking for. They want you to solve for Y. The variable, the letter that they say solve for is the one that you want to get by itself. Now, because you have two terms, one an X term, the other one's a Y term because you want to get the Y term all by its lonesome, you want to get rid of the terms that have nothing to do with Y on that side. That brings us to 3x because the 3x has nothing to do with the Y. It's time to move it over. The 3x is being added here, so we want to do the opposite operation always by moving the 3x over. So you move the...subtract 3x on this side, but for any equation, you want to preserve the balance, so you want to subtract 3x on the other side as well. So as a result, you're going to have 14y is equal to 2 minus 3x. Now, the time has come for you to solve for Y. Get Y by itself. Isolate it, if you will. Look at the operation that's connecting Y with 14. It's multiplication. With solving any equation, always do the opposite operation. Because this is multiplication that's sticking them together, the opposite operation is divide. So divide this by 14, but for the sake of a balance, divide the other side by 14. So therefore, the 14 divided by 14 on the left side cancels out. You have a Y and the 14 doesn't really reduce with a 2 or 3 together, so you want to leave the right side as it is. So therefore, solving for Y gives you 2 minus 3x over 14. I hope that gives you some insight, and my name is Jimmy, and that is an example as to how you solve algebraic equations."