Basic Algebra

Working with positive and negative numbers

Order of Operations

Combining Like Terms

Distributive Property

Equations

Shortcuts/tips: when you add two positives, the result is positive. When you add two negatives the result is negative. When you add a negative and a postive the sign is determined by the largest addend.

Two Positives: 5+19= 24

Two Negatives: -3+-2= -5

Positive and Negative: -12 + 7= -5 or 6 + -2 = 4

Shortcuts/tips: the number that is being subtract is assumed to be positive unless a tiny - is indicted. when this happens change both the subtraction and the subtrahead's negative sign to positive.

-8 - -2= -6 (-8 + +2= -6)

5 - 6 = -1

-8 - 12 = -4

6 - 4 = 2

Shortcuts/Tips: if both are positive the result will be positive, if both are negative the result will be positive, if one is negative and the other is positive the result will be negative

9 x 5 = 45

-3 x 10 = -30

-12 x -6 = 72

-33 / 3 = -11 ( / denotes division symbbol)

-14 / -2 = 7

8 - 6 = 2

12 + 15 + 2 =29

Examples:

6x + 2x = 8x

8x + 7y - 5y=

8x + 2y

12x + x = 13x

13x - 3 + 5 =

13x + 2

24x + 1 = 25

you want to get rid of the 1. the opposite of addition is subtraction, subtract one. this cancels out the 1 on the left side. now you must subtract one from the other side of the problem. RULE: what you do to one side of the problem must be done to the other. so:

24x + 1 - 1 = 25 - 1 =

24x = 24

now we have the term by itself, but we're not finished. we're solving for x, so we need to get rid of the 24. we do this by division, the opposite of multiplication. 24x means x times 24. so:

24x/ 24 = 24 / 24 =

x = 1

when you have the variable by itself you have solved the problem. in this cause x equals 1. I have few example problems of varing difficulty, with tips on how to solve the more difficult ones

1) remember / is a division symbol.

2x = 24

2x / 2 = 24 / 2

x = 12

Fairly simple. There were no other steps so you just have to get rid of the coefficient. Moving on

2) \ is used for fractions, * is for multiplication

4\7x - 1 = 11

4\7x - 1 + 1 = 11 + 1 =

4\7x = 12

Now how do you get rid of a fraction? Easy! Use the reciprocal, in other words flip the fraction upside down and then multiply

4\7x * 7\4 = 12 * 7\4 =

x = 84\4

then just divide the numerator by the denominator, aka the top number by the bottom number. so:

x = 21

3) variables on both sides of the problem

11x + 5 = 2x - 4

11x + 5 - 5 = 2x - 4 - 5

11x = 2x - 9

You've gotten rid of the 5. Now what? As stated before, you want the variable you are solving for on one side of the problem, so you want the 2x on the left side. How? subtract!

11x - 2x = 2x - 2x - 9

9x = 9

9x/9 = 9/9

x = 1

4) using distributive property

4x + 2 = 2(x+3)

first things first, get rid of the parenthesis! using the distributive property rule....

4x + 2 = 2x + 6

much better! now using what you've (hopefully) learned let's see what we can do

4x + 2 - 2 = 2x + 6 - 2

4x = 2x + 4 =

4x - 2x = 2x - 2x + 4

2x = 4

2x/2 = 4/2

x = 2

Good! While this make take up a lot of space on your notebook page, it's neat and if you do make a mistake it's a lot easier to find it.