Page 119 - Algebra 1

The Addition and Subtraction Properties of Equality hold for every real number a, b, and c.
Addition and Subtraction Properties of Equality
Addition Property of Equality
You can add the same number to both sides of an equation and the statement will still be true.
Examples 2=2 a=b 3+2=2+3 a+c=b+c
5=5
Subtraction Property of Equality
You can subtract the same number from both sides of an equation and the statement will still be true.
Examples 10 = 10 a = b
10 - 4 = 10 - 4 a - c = b - c
6=6
On the first page of the lesson the Subtraction Property of Equality is illustrated with balance scales. Below, the Addition Property of Equality is illustrated.
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9=9 2+9=9+2
Inverse operations are operations that undo each other. To solve an equation, isolate the variable on one side of the equal sign by using inverse operations. Use the same inverse operation on each side of the equation.
Inverse Operations
Addition Subtraction Multiplication Division
Exploration Using Algebra Tiles to Model One-Step Equations Use algebra tiles to model x + 6 = 9.
a. Model each side of the equation.
b. Isolate the x-tile. Add six negative 1-tiles to both sides. Remove pairs
that equal zero.
c. What is the solution?
d. Use algebra tiles to model x - 2 = 4. What is the solution?
Materials
algebra tiles
Hint
The + and – algebra tiles that are the same shape are opposites and undo each other.
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104 Saxon Algebra 1