Distributive Property and Solving for a Variable:


Part One:


To finally solve for a variable means that you want to get that variable by itself. To do so you have to the exact opposite operation, don't forget whatever you do to one side you ave to do to the other. Here are steps to help you solve an equation on your own.

Step 1:
Multiply the term that is on the outside of the bracket to the each term that is on the inside of the bracket. *Don't forget your integer rules*. When you are multiplying through the brackets and you come apon a negative number, when your number on the outside of the brackets is positive, your out come of that will be a negative number. If that sounded a bit confusing to you look below for further examples;

Value Outside of bracket - Value on inside of bracket = Value outcome

+ x + = +
- x - = +
+ x - = -
- x + = -
Finding the signs correctly is key to distributive property!!!!!


Step 2:
Then collect like terms and add or subtract terms. Make sure your variables are the left side of the equation.


Watch this video for extra information on distributive property and solving for a variable.



Part 2:
Examples of applying distributive property.

Example 1:
4(x-1)=36
=4x-4=36
=4x-4+4=36+4
4x=40
4x/4=40/4
x=10

Example 2:
3(x-2)=21
=3x-6=21
=3x-6+6=21+6
=3x/3=27/3
x=9


Example 3:
2x-3(2x-3)+4=33
=2x-6x+9+4=33
=-4x+13-13=33
=-4x=20
=-4x/-4=-4/20
x=-5

Example 4:
-2(2x-4)+3(X+2)=15
-4x+8+3x+6=15
-x+14=15
-x+14-14=15-14
-x=1

Part 3:
Practice all that you learned on the following 4 questions.

a) 3(2x+1)-5(x+1)=4


b) 4(x-7)-2(x-5)=-4x


c)4x+2x-3x=27


d)4(4x+3)=44