One of the most important topics covered in Algebra 1 is how to solve linear equations. The process of solving linear equations is so important because it’s extremely useful in real life and can be used to solve several different types of problems that come up on a regular basis.
When you first learn arithmetic, you start out by solving equations that look like this: number operation number equals unknown. Some examples of this format include 2 + 2 = ?, 5 * 4 = ? and 14 – 8 = ?. In all of these cases, being able to solve the equation is a direct result of knowing how to use the operation. What I mean by this is that if you’re trying to solve 12 + 6 = ?, then you can do this just by knowing how to use addition.
Algebra introduces variables that can take the place of numbers. This allows you to move around the unknown in the equation, so you might end up with something that has a format of number operation unknown equals number. An example of this would be 6 + x = 17. When you’re solving linear equations, knowing how to use the operation isn’t enough to figure out the answer. Instead, you have to apply a small amount of logic to change the equation into something you know how to figure out.
The main logic trick that you learn that helps you to solve these equations is that you can perform the same operation to both sides of an equation. If you have 6 + x = 17, for example, then you learn that you can subtract six from both sides if you want to. If we subtract six from both sides, we get 6 + x – 6 = 17 – 6, which simplifies to x = 11. By adding this single idea, we can go from solving basic equations by just knowing how to use the operations to solving more complicated linear equations.
Later on, you get more complicated equations that look something like 2x + 7 = 1, and you have to use your trick more than once. You’ll start out by subtracting seven from both sides and you’ll get 2x + 7 – 7 = 1 – 7 which simplifies to 2x = -6. Then you’ll divide by two on both sides to get 2x / 2 = -6 / 2 to get x = -3. The process of solving linear equations like these is pretty straight-forward, but you have to be comfortable with using the operations on integers and you have to understand how to use the both sides trick.