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Ch 8 Equations and Inequalities
8.1 Solving Equations with Rational
Coefficients
Algebraic Equation
• Has an equal sign and a variable
• Directions: Solve
• Solution: a value for the variable that makes
the equation true
Properties of Equality
Multiplication Property of
Equality
ab
ca  cb
Division Property of Equality
ab
a b

c c
Inverse Operations
• Undo each other
• To under multiplication use the:
Division Property of Equality
• To under Division use the:
Multiplication Property of Equality
1
7
x
Example 1: Solve
2
 2  7 1  2 
Hint:

x 


When you  1  1
2  1 
divide
fractions
multiply
by its
reciprocal
14  x
Example 2: Solve
6
3
m
7
14
7 6
7 3
 m 
6 7
6 14
2
2
-1
1
m
4
Example 3: Solve -19.6 =5.6x
19.6 5.6 x

5.6
5.6
3.5  x
Example 4: Solve -20.9y = -250.8
20.9 y 250.8

20.9
20.9
y  12
Example 5: Kipton spent $116 on boxes of
baseball cards. He paid $14.50 per box. Write
and solve an equation to find how many boxes
of cards Kipton bought.
(price per box) ( Number of boxes) = Total
(14.5)(b) =116
14.5b 116

14.5 14.5
b  8boxes
Homework
• Page 327 (12-40) even