170 Chapter 3 Solving Equations Addition and Subtraction Properties of Equality ax b c a 0. The Addition and Subtraction Properties of Equality Let a, b, and c represent algebraic expressions. 1. The addition property of equality: If a b, then a c b c 2. The subtraction property of equality: If a b, then a c b c 5142 7 13 20 7 13 13 13 Example 4 To solve the equation t 12 3, use the addition property of equality. The solution is 9. t 12 3 t 12 12 3 12 t 9 Example 5 To solve the equation 1 p 2, use the subtraction property of equality. 1 p 2 1 2 p 2 2 3 p The solution is 3. Section 3.2 Key Concepts An equation is a statement that indicates that two quantities are equal. A solution to an equation is a value of the variable that makes the equation a true statement. Definition of a Linear Equation in One Variable Let a, b, and c be numbers such that A linear equation in one variable is an equation that can be written in the form Two equations that have the same solution are called equivalent equations. Examples Example 1 3x 4 6 is an equation, compared to 3x 4, which is an expression. Example 2 The number 4 is a solution to the equation 5x 7 13 because when we substitute 4 for x we get a true statement. ✓ Example 3 The equation 5x 7 13 is equivalent to the equation x 4 because they both have the same solution, 4.
miller_prealgebra_2e_ch1_3
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