CRAZY EQUATIONS!!!

3(x-5) = -7x + 12

If you are like me, you panic when this equation is thrown in front of you; however, HAVE NO FEAR! There is a simple way to solve this crazy equation. Let's do it step-by step. Each picture below illustrates a step in the process of solving this equation with a variable on each side.

Here is our original equation. I learned to set it up like a table, to keep my steps organized.

To begin, the 3 must be distributed to everything in the parentheses. 3 multiplied by X is 3x, and 3 multiplied by -5 is -15. Copy down the rest of the equation.
This cannot be solved until all X's are on the same side of the equals sign. I could either subtract 3x from the left, or add 7x to the right. I like working with whole numbers, so I chose to add seven. Copy down your new equation.
Now that all X's are on the same side of the equal sign, we need to isolate it. This happens by performing the opposite of subtraction, which is multiplication. Add 15 to both sides of the equation remembering that anything that happens to one side of an equation, must happen to the other.
Good work. We are close to finished, but we haven't isolated our variable. 10 is being multiplied by X here, so we will perform the opposite and divide by 10 on both sides of the equation.

CONGRATULATIONS MASTER OF CRAZY EQUATIONS!!!

Direct and Inverse Variation

Direct and Inverse Variation are two very important concepts to know in Algebra 1, as well as future math classes. We'll start with Direct variation. In direct variation, an equation formula such as y=kx will be used. This means, that there is a constant number that can be multiplied by an X value to get a Y value. As X increases, so does Y. When you divide the increase in Y by the increase in X, you get your constant, or K. Take a look at the below picture:

As, for Inverse Variation, it's a little different. We use the equation y=k/x to solve. You can always divide the constant by the X value to get a Y value. When the X value increases, the Y value decreases. Take a look at this example:

HAPPY LEARNING!