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Multiplying Each Side of an Equation
EXAMPLE 2
x
5
Solve = º30.
SOLUTION
On the left side of the equation, x is divided by 5. You can isolate x by
multiplying each side by 5 to undo the division.
x
= º30
5
Write original equation.
冉 5x 冊
5 = 5(º30)
STUDENT HELP
Look Back For
help with reciprocals,
see page 108.
Multiply each side by 5.
x = º150
..........
Simplify.
2
3
When you solve an equation with a fractional coefficient, such as 10 = ºm,
you can isolate the variable by multiplying by the reciprocal of the fraction.
Multiplying Each Side by a Reciprocal
EXAMPLE 3
2
3
Solve 10 = ºm.
SOLUTION
2
3
10 = ºm
冉º32冊10 = 冉º32冊冉º23m冊
º15 = m
..........
Write original equation.
3
Multiply each side by º}}.
2
Simplify.
The transformations used to isolate the variable in Lessons 3.1 and 3.2 are based
on rules of algebra called properties of equality.
CONCEPT
SUMMARY
P R O P E RT I E S O F E Q UA L I T Y
ADDITION PROPERTY OF EQUALITY
If a = b, then a + c = b + c.
SUBTRACTION PROPERTY OF EQUALITY
If a = b, then a º c = b º c.
MULTIPLICATION PROPERTY OF EQUALITY
If a = b, then ca = cb.
DIVISION PROPERTY OF EQUALITY
If a = b and c ≠ 0, then = .
a
c
b
c
You have been using these properties to keep equations in balance as you solve
them. For instance, in Example 2 you used the multiplication property of equality
when you multiplied each side by 5.
3.2 Solving Equations Using Multiplication and Division
139