1. Algebra II September 8, 2005

2. Drill (solve for each variable)1) 2) 3)

3. Objective
Today we will learn to use the rules of combining like terms and the distributive property to solve equations.

4. Combine Like Terms
In order to combine like terms the terms must have the exact same variable expression or simply have no variable expression in them.

5. Examples
2x and 3x are like terms because they have the same variable expression.
2a and are not like terms because they do not have the same variable expression.

6. Rules
Once you find your like terms you either add or subtract the coefficients (the numbers in front of the variables) and the variable expressions stay the same.

7. Examples
1) 2x + 3x + 6a – 2a + 2x
2) 3s +
3) 4a – 2b + 4a – 3b + 3c

8. Distributive Property
Anytime you have a number or expression next to parentheses it means to multiply the number or expression by each term inside of the parentheses.

9. Step one 5 multiplied by 2x is equal to 10x
Examples
5(2x + 3)
Step one 5 multiplied by 2x is equal to 10x
Step two 5 multiplied by a +3 is +15
Therefore 5(2x + 3) is 10x +15

10. Step one -3 multiplied by 8x is equal to -24x
Examples
-3(8x – 4)
Step one -3 multiplied by 8x is equal to -24x
Step two -3 multiplied by a -4 is +12
Therefore -3(8x – 4) is -24x +12

11. 4(3x + 2) = 32 4(3x) + 4(2) = 32 12x + 8 = 32 - 8 -8 12x = 24 x = 2
Examples
4(3x + 2) = 32
4(3x) + 4(2) = 32
12x = 32
12x = 24
x = 2

12. Algebra Word Problems
Ex: 3 times the sum of 2 times a number and 4 is equal to 36.
Write an equation to represent the word problem
SOLVE

13. Classwork
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#’s 43, 44, 47 – 54
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