Download Ch2-Sec 2.2

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2.2 – Slide 1
Chapter 2
Equations, Inequalities, and
Applications
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2.2 – Slide 2
2.2
The Multiplication Property of
Equality
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2.2 – Slide 3
2.2 The Multiplication Property of Equality
Objectives
1.
2.
Use the multiplication property of equality.
Simplify, and then use the multiplication property of
equality.
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2.2 – Slide 4
2.2 The Multiplication Property of Equality
Using the Multiplication Property of Equality
Multiplication Property of Equality
If A, B, and C (C is not equal to 0) represent real
numbers, then the equations
A=B
and
AC = BC
are equivalent equations.
In words, we can multiply each side of an equation
by the same nonzero number without changing the
solution.
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2.2 – Slide 5
2.2 The Multiplication Property of Equality
Using the Multiplication Property of Equality
Example 1
Solve.
3x = 42
⅓ · 3x = ⅓ · 42
x = 14
Multiply both
sides by ⅓.
Check: 3 · 14 = 42
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Note: The multiplication
property of multiplication
also permits dividing
each side of an equation
by the same nonzero
number. Here we could
have also solved this
equation by dividing both
sides by 3 (since this is
equivalent to multiplying
by ⅓).
2.2 – Slide 6
2.2 The Multiplication Property of Equality
Using the Multiplication Property of Equality
Note
In practice, it is usually easier to multiply on each
side if the coefficient of the variable is a fraction, and
divide on each side if the coefficient is an integer or a
3
decimal. For example, to solve  x  12,
4
4
3
it is easier to multiply by  , the reciprocal of  , than to
3
4
3
divide by  . On the other hand, to solve
4
–5x = – 20,
1
it is easier to divide by – 5 than to multiply by  .
5
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2.2 – Slide 7
2.2 The Multiplication Property of Equality
Using the Multiplication Property of Equality
Example 2
Solve.
5
(b) z  3
6
(a) –1.5y = 7.5
1.5 y 7.5
=
1.5 1.5
Divide both
sides by –1.5.
y = –5
Check: –1.5 · –5 = 7.5
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6 5
6
 z  3
5 6
5
z
Check:
18
or 3.6
5
5 18
 3
6 5
2.2 – Slide 8
2.2 The Multiplication Property of Equality
Simplifying and Using the Multiplication Property of Equality
Example 3
Solve.
5a – 13a = 56
– 8a = 56
First combine like terms.
8a 56
=
8 8
Then solve.
a = –7
Check: –8 · –7 = 56
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2.2 – Slide 9