# 04D DistributingSolvingEquations

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```					  Algebra 2 w/ Trig
Lesson 4

Distributive Property,
Solutions of Equations
Distributive Property
a(b + c) = a∙b + a∙c = ab + ac

i.e.     5(3x + 2) = 15x + 10

7(x + 4) = 7x + 28
Expand by distribution:
2a-4b0    2ab2 c a-2 
c       x 2 - b-4 
            
First, move all the variables to the numerator.
2a-4 c-1 2ab2cx-2 - a-2b4 
Now distribute.

4a b x -2a b c
-3 2    -2      -6   4 -1
Toolbox 1: Distribute
4a2  b-2 3ba 
b  a 4 - a2 


4a b
2 -1
a    b - 3a b 
-4 -2   -1

4a b -12a
-2 -3
# 12
Solutions of Equations
   Solving Equations:
ISOLATE VARIABLE TERM!
   1. Eliminate parentheses (distribute).
   2. Add like terms on both sides.
   3. Get variable terms on one side and
constant terms on the other side.
(change sides = change signs)
Transposition
   4. Eliminate the coefficient of the
variable term by multiplying or dividing.
Solve for x:
12  2x  5   2   x  3

12 -2x - 5  2 + x - 3
-2x + 7  x  5
12  3x

x4
Toolbox 2: Solve
1 3        1      
2 - x      x  2
8 2        4      
1       1
- 3x  x  2
4       4
Eliminate the fractions by multiplying the
entire equation by the common denominator.
1      1      
4  - 3x  x  2 
4      4      
1-12x  x  8

9  13x
9
x=
13
# 6, 8, 10
Assignment:
Problem Set 4
Replace # 14 Find the perimeter of a 120
degree circular sector region that has a radius
of 8 inches.
Replace # 18 find the area of a 150 degree
circular sector that has a radius of 12 inches.

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