How to do Algebra

Math Madness!

In this booklet, you will learn how to solve the elaborate mathematical equations that are in Algebra 1 and in Pre-Algebra. You will be able to use what you used in this booklet in everyday life. Remember well.

IT”S ALRIGHT TO ENJOY IT TOO, YOU KNOW!!!
This is a funny cartoon that has something to do with math-at least, I think it is funny.

Table of Contents:
How to Solve One-Step Equations: Page 3

How to Solve Two-Step Equations: Page 4

How to Solve Equations With Variables on Both Sides: Page 5

How to Combine Like-Terms in an Equation: Page 6

How to use the Distributive Property:
Page 7 and 8
How to solve One-Step Equations:
This is your equation:
7x + 12 = 54
First, you subtract the opposite of the constant from the constant, in other words, you have to add the opposite, (-6) to six, therefore canceling it out. This is what your equation looks like when you are doing this process:
7x + 12 = 54
    -12  -12
        0   42
In the end, your new equation is 7x=42. You divide each side by the number in front of the variable, in this case, 7. That cancels out the 7 in 7x, leaving just x. When you divide 42 by seven, you get 6, so the equation is now x=6, which is your answer.


How To solve two-step equations:

This is your equation:
5x + 42 = 53 - 6x

First, you have to combine any like-terms, if there is any. In this case, there isn’t any. Then, you need to add the opposite of one of the variables to itself and then to the other variable on the other side. This is what your equation looks like when you are doing this:
   5x + 42 = 53 - 6x
+6x                +6x
11x               0
This is your equation now:
11x + 42 = 53

Now, do the same to the other side, (the one without the variable).

11x + 42 = 53
       -42   -42
         0     11
Your equation is now 11x=11. Now, you divide each side by the number in front or the variable, just as you did in One-Step equations. Your answer is x=11.

how to solve equations with variables on both sides:

This is your equation:
7x=8x+10

As you can see, there are variables on both sides of this equation. First, you need to add the opposite of 8x, (or the coefficient on the side with the constant), to the side with only the coefficient on it. This is what your equation looks like while you are doing this process:

7x = 8x+10
-8x  -8x
-x      0

Now the equation is -x=10. You can’t have a -x, so you have to divide each side by -1. The equation is now x = -10. That is your answer.

How to Combine Like-Terms in an Equation:


This is your equation:
9x + 19x = 28

First, you have to combine like-terms. In order to do that, you need to add any constants or coefficients that are on one side of the equation to each other. So, the problem is now:

28x = 28

Divide both sides by the coefficient left, and your answer is x=1.


How to use the Distributive Property:

This is your Equation problem:
9(x-3) + 14 = 42 - 12x + (-6)

This one is more complicated. First, you need to combine like-terms, (as always) but in order to do that you need to use the distributive property part of the equation, 9(x-3), and simplify, (or solve) it. You need to multiply nine (or whatever number is outside the parentheses by the two numbers inside the parentheses. Don’t worry about the subtraction, (or addition) sign, instead of thinking it is an addition or subtraction sign, keep saying to yourself, it’s positive, or in this case, it’s negative. So all you need to do is multiply nine by x, (9x), then multiply nine by -3, (-27).
This is your new equation, (with the distributive property gone):
9x - 27 + 14 = 42 - 12x + (-6)
Once more, you need to combine like terms. On the left side of the equation you need to combine the terms -27 and 14. So, add 14 to -27 (-13) and you don’t need to simplify that side any further.
Now, you need to simplify the other side. This is the side of the equation you need to be looking at:
42 - 12x + (-6)
In order to simplify it further, you need to add 42 with -6. The answer to that is 36. So, your equation is now -12x = 36. Once again, divide both sides by -12, (the coefficient), and 36/-12 is -3. Your answer is x=-3.