Section 2.1 Addition, Subtraction, Multiplication, and Division Properties of Equality 103 Answers 5. e 6. 519.66 11 12 f Applying the Addition and Subtraction Properties of Equality Example 3 Solve the equations. 9 4 3 4 a. q b. Solution: a. 1 02 34 34 34 1.2 z 4.6 To isolate q, add to both sides . Simplify. 9 4 3 4 12 4 q q 3 4 3 4 q 0 3 4 3 q or equivalently, q 3 Check: Substitute . 9 4 9 4 q 3 3 4 3 4 q 3 Common denominator 9 4 9 4 12 4 9 3 4 9 4 The solution set is {3}. ✔ True b. 4 To isolate z, add 1.2 to both sides. Check: Substitute . 1.2 z 4.6 1.2 1.2 z 4.6 1.2 0 z 5.8 z 5.8 1.2 z 4.6 1.2 5.8 4.6 4.6 4.6 z 5.8 The solution set is {5.8}. ✔ True Skill Practice Solve the equations. 5. 6. 8.1 w 11.5 1 4 a 2 3 3. Multiplication and Division Properties of Equality Adding or subtracting the same quantity to both sides of an equation results in an equivalent equation. In a similar way, multiplying or dividing both sides of an equation by the same nonzero quantity also results in an equivalent equation. This is stated formally as the multiplication and division properties of equality. TIP: The variable may be isolated on either side of the equation.
miller_beginning_intermediate_algebra_4e_ch1_3
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