Section 2.2 The Addition Property of Equality 103 This property tells us that if two expressions are equal, we can • add the same number to both expressions and the expressions will remain equal. • subtract the same number from both expressions and the expressions will remain equal. Example 2 illustrates the most basic use of the addition property of equality. We will use this property to solve for the variable in one step. ���������������������� Using the Addition Property of Equality to Solve an Equation Step 1: Determine the operation that will isolate the variable on one side of the equation. Perform this operation on each side of the equation. Remember the inverse property for addition: a + (-a) = -a + a = a - a = 0. Step 2: Simplify each side of the equation, as necessary. The result should be of the form x = some number or some number = x Step 3: Check the solution by substituting the value into the original equation. Step 4: Write the solution in set notation. �� ������������������������ ������������������ Solve each equation using the addition property of equality. Check each answer. 2a. x + 12 = 10 2b. y - 7 = -13 2c. b + 1 2 =- 3 2 2d. 1.8 = 2.1 + r Solutions 2a. x + 12 = 10 x + 12 - 12 = 10 - 12 Subtract 12 from each side. x=-2 Simplify. Check: x + 12 = 10 Original equation -2 + 12 = 10 Replace x with -2. 10 = 10 Simplify. Since x = -2 makes the equation true, the solution set is {-2}. 2b. y - 7 = -13 y - 7 + 7 = -13 + 7 Add 7 to each side. y = -6 Simplify. Check: y - 7=-13 Original equation -6 - 7=-13 Replace y with -6. -13=-13 Simplify. Since y = -6 makes the equation true, the solution set is {-6}. 2c. b + 1 2 =- 3 2 b + 1 2 - 1 2 =- 3 2 - 1 2 Subtract 1 2 from each side of the equation. b=- 4 2 Simplify each side. b=-2 Simplify the fraction.
hendricks_beginning_algebra_1e_ch1_3
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