Page 22 - Math Course 2 (Book 1)

Solving Algebraic Equations

Mo. 1

Lesson 4 Key Concept

Subtraction Property
KEY CONCEPTS: of Equality
1. Solve equations by using the Subtraction
Property of Equality. Words If you subtract the same number from
2. Solve equations by using the Addition each side of an equation, the two sides
Property of Equality. remain equal.

Symbols For any numbers, a, b, and c if a = b,
then a – c = b – c.
MO. 1 - L4a Example 5 = 5 x + 2 = 3

Property of Equality: 5 – 3 = 5 – 3 x + 2 – 2 = 3 – 2
2 = 2
x = 1
Adding and Subtracting

Vocabulary A-Z Addition Property
of Equality
Let us learn some vocabulary
Words If you add the same number to each
side of an equation, the two sides
remain equal.

Inverse Operation Symbols For any numbers, a, b, and c if a = b,
then a + c = b + c.
Inverse operations “undo” each other. You can use Example 6 = 6 x – 2 = 5
inverse operations to solve the equation. 6 + 3 = 6 + 3 x – 2 + 2 = 5 + 2

9 = 9 x = 7
x + 4 = 7 To undo the addition of 4 in the
expression x + 4, you would subtract 4.

Subtract 4 from x + 4 – 4 = 7 – 4 Subtract 4 from
the left side of the right side of
the equation x + 0 = 3 the equation to Let’s Begin
to isolate the keep it
variable x = 3 balanced

Operation Inverse Operation Solve Equations by Subtracting
+ –
– +
Example

Solve x + 4 = – 3. Check your solution and graph it
Equivalent Equations on a number line.

x + 4 = –3 Write the equation.
Equations that have the same value.
x + 4 – 4 = –3 – 4 Subtract 4 from each side.
x + 4 = 7 x = 3
x + 0 = –7 4 – 4 = 0, –3 – 4 = –7
These are both equivalent expressions
because they have the same value, 3 x = –7 Identity Property; x + 0 = x

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