Page 25 - Math Course 2 (Book 1)

Solving Algebraic Equations

Mo. 1

Lesson 5 Key Concept

Division Property
KEY CONCEPTS: of Equality
1. Solve equations by using the Division
Property of Equality. Words When you divide each side of an
2. Solve equations by using the Multiplication equation by the same nonzero number,
the two sides remain equal.
Property of Equality
Symbols For any numbers, a, b, and c, where
a b
c = 0, then =
MO. 1 - L5a c c
Example 14 = 14 3x = –12
Property of Equality: 14 14 3x = –12
=
3
Multiplying and Dividing 7 2 = 2 7 3 x = –4

Vocabulary A-Z Multiplication Property

Let us learn some vocabulary of Equality
Words When you multiply each side of an
equation by the same number,
the two sides remain equal.

Inverse Operation Symbols For any numbers, a, b, and c, if a = b,
then ac = bc
Inverse operations “undo” each other. You can use
inverse operations to solve the equation.
Example 8 = 8 x = 7
11x = 77 To undo the multiplication of 11 in 8 (–2) = 8 (–2) 6
(
the expression 11x, you would divide by 11. –16 = –16 ( x 6 = (7)6
6
x = 42
11 x = 77
11x 77
=
11 11 Let’s Begin

1x = 7
Divide the left side x = 7 Divide the side side
of the equation of the equation
by 11 to undo the by 11 to keep it
multiplication balanced. Solve Equations by Dividing
11• x.

Example

Operation Inverse Operation Solve 7x = –56. Check your solution and graph it on
x / a number line.
/ x
7x = –56 Write

7(x) –56 Divide each side by 7 to undo the
=
7 7 multiplication in 7 • x.
7 –56
1x = –8 = 1, = –8
7 7
x = –8 Identity Property; 1x = x

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