Download 1.3 Solving Equations

1.3 Solving Equations
Remember those good ‘ol times
last year in Geometry???
Algebraic Properties of
Equality
Addition Property
If a=b, then a+c = b + c
Subtraction Property
If a=b, then a-c = b-c
Multiplication Property
If a=b then ac = bc
Division Property
If a=b and c does not = 0, then
a c  b c
Algebraic Properties of Equality
Reflexive Property
For any real number a, a = a
Symmetric Property
If a =b, then b=a
Transitive Property
If a=b and b=c, then a=c
Substitution Property
If a=b, then a can be substituted for b in any
equations or expression
SOLVING EQUATIONS
THE GOLDEN RULE:
Do unto one side of the equation what you do to the other.
Or: The “I Want Cake Too” Theorem
3(x – 5) + 1 = 2x – 4
3x – 15 + 1 = 2x – 4
3x – 14= 2x – 4
3x = 2x +10
x = 10
Given
EX – multistep equation
2
3
4
x   1 x
5
7
7
2
3
4
35  ( x   1  x )
5
7
7
35  2
35  3
35  4
x
 35 
x
5
7
7
14x  15  35  20x
34x  20
20 10
x

34 17
FRACTION BUSTING
Magic # = -35
EX – solving formulas
Solve for b1
1
A  h(b1  b 2 )
2
2A  h(b1  b2 )
2A  h  b1  h  b2
2A  h  b2  h  b1
2A  h  b 2
 b1
h
OR
2A
 b1  b 2
h
2A
 b 2  b1
h
Ex – solving formulas again
Solve for x
ax – y + bx = cx + yx
ax – cx – yx – y + bx = 0
ax – cx – yx + bx – y = 0
ax – cx – yx + bx = y
x(a – c – y + b) = y
y
x
ac y b