Page 44 - Math Course 1 (Book 2)

Linear Equations: Multiplication and Division

Mo. 8

Lesson 3

KEY CONCEPTS:
1. Solve equations by using multiplication.
2. Solve equations by using division Let’s Begin

Solve Using Multiplication by a Positive Number

MO. 8 - L3a
Example
Solving Equations:
s
Multiplication Solve = 3. Check your solution.
12

s
Key Concept 12 = 3 Original equation

Multiply each side by 12.
Multiplication Property of Equality

Words If an equation is true and each side
is multiplied by the same number, the
resulting equation is true. Answer and

Symbols For any numbers a, b, and c, if a = b,
then ac = bc.
Solve Using Multiplication by a Fraction
Examples 6 = 6 9 = 9
6 x 2 = 6 x 2 9x(–3) = 9x(–3) Examples
12 = 12 –27 = –27

1 1 3 2
10 x = 10 x Solve –1 k =
2 2 8 3

Original Equation
Solve –75 = –15b.
Rewrite the mixed number
–75 = –15b Original equation as an improper fraction.
8
Multiply each side by –
1 11 11
1 1 Multiply each side by – the reciprocal of –
– (–75) =– (–15b) 15 8
15 15 the reciprocal of –15

Answer 5 = b Check this result. Answer check this result

16
To check that 5 is the solution, substitute 5 for b in To check that – is the solution, substitute
the original equation. 16 33
– for k in the original equation.
33

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