Applying the Multiplication Property of Equality Solve the equation by using the multiplication property of equality. Solution: is equivalent to Simplify. Check: d 6 1 6 d 4 d 24 4 d 6 24 6 4 4 4 6 1 The solution is 24. ✔ True It is important to distinguish between cases where the addition or subtraction properties of equality should be used to isolate a variable versus those in which the multiplication or division property of equality should be used. Remember the goal is to isolate the variable term and obtain a coefficient of 1. Compare the equations: In the first equation, the relationship between 5 and x is addition. Therefore, we want to reverse the process by subtracting 5 from both sides. In the second equation, the relationship between 5 and x is multiplication. To isolate x, we reverse the process by dividing by 5 or equivalently, multiplying by the reciprocal, 5 x 20 and 5x 20 5x 5 20 5 5 5 x 20 5 x 15 x 4 15 . 5 x 20 and 5x 20 1d 24 1 6 d 4 6 1 1 6 d. d 6 4 d 6 4 Example 7 Section 2.1 Addition, Subtraction, Multiplication, and Division Properties of Equality 127 61 16 To obtain a coefficient of 1 for the d-term, multiply by the reciprocal of , which is . Skill Practice Solve the equation. 17. x 5 8 Classroom Example: p. 130, Exercise 42 Instructor Note: Remind students that dividing by a number is the same as multiplying by its reciprocal. Thus, d 6 1 6 d Answer 17. 40
miller_introductory_algebra_3e_ch1_3
To see the actual publication please follow the link above