Goal: Be able to solve medium to hard equations including fraction busters.
To help solve linear equations always try to produce equivalent fractions by these properties. 

Addition property of equality.
Add same number to both sides. 
If a=b then a-c = b-c

Subtraction Property of Equality
If a=b then a-c = b-c 

Multiplication Property of Equality 
Multiply both sides by non-zero
If a=b then, a x c = b x c 

Division Property of Equality
Divide both sides by the same non-zero number.
If a=b, then a/c = b/c 

Ex. 1: x+5= -7 
Use subtraction Property of Equality to  -5 from both sides.
x= -7-5 = x= -14.

Ex. 2: 4x + 7 =27
Use subtraction Prop. of Equality to both sides to isolate 4x.
Then when you get 4x=20, you can use Division Property of Equality to divide 4 to both sides. 
20/4 = 5=x

Ex. 3: Now to solve equations with variables on both sides.
2b + 11= 15 - 6b
Use subtraction property to get a variable on one side. So minus 2b to both sides to get: 11= 15 - 8b.
Again use subtraction property to -15 to both sides to get: -4= -8b.
Finally use the division property of equality to divide -8 to both sides and get b= 1/2/

Ex. 4: Solving equations with fractions.
3/4x - 2/3 = 5/6 
Find LCM (Lowest Common Multiple) of all fractions, which is 12. Then multiply 12 to all the fractions. After that you will eventually get:
9x - 8 = 10
So now that there is no fractions it is easier to solve. 
Use addition property of equality to add 8 to both sides to get:
9x = 18
Then divide both sides by 9 to get x= 2.


Problems for you to try! 

1. 7/2x - 1 = 2x + 5

2. 3/4(4/5x - 2) = 11/4