Fundamentals of Mathematics, 2008a

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11.5 Solving Equations of the Form ax=b and x/a=b 5
11.5.1 Section Overview
• Multiplication/ Division Property of Equality
• Combining Techniques in Equations Solving
11.5.2 Multiplication/ Division Property of Equality
Recall that the equal sign of an equation indicates that the number represented by the expression on the left
side is the same as the number represented by the expression on the right side. From this, we can suggest
the multiplication/division property of equality.
Multiplication/Division Property of Equality
Given any equation,
1. We can obtain an equivalent equation by multiplying both sides of the equation by the same nonzero
number, that is, if c ≠ 0, then a = b is equivalent to
a · c = b · c
2. We can obtain an equivalent equation by dividing both sides of the equation by the same nonzero
number, that is, if c ≠ 0, then a = b is equivalent to
a
c = b c
The multiplication/division property of equality can be used to undo an association with a number that
multiplies or divides the variable.
11.5.2.1 Sample Set A
Use the multiplication / division property of equality to solve each equation.
Example 11.26
6y = 54
6 is associated with y by multiplication. Undo the association by dividing both sides by 6
6y
6 = 54 6
9
)6y
= )54
)6
)6
y = 9
Check: When y = 9
6y = 54
becomes
,
a true statement.
The solution to 6y = 54 is y = 9.
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