Section 2.1 Addition, Subtraction, Multiplication, and Division Properties of Equality 125 The division property of equality can also be used to solve the equation by dividing both sides by the coefficient of the x-term. In this case, divide 5x 15 both sides by 5 to make the coefficient of x equal to 1. Divide by 5. The coefficient on the x-term is now 1. 5x 15 5x 5 15 5 1x 3 x 3 Applying the Division Property of Equality Example 4 Solve the equations using the division property of equality. a. 12x 60 b. 48 8w c. x 8 Solution: a. To obtain a coefficient of 1 for the x-term, divide both sides by 12. Simplify. Check: 12x 60 12152 60 60 60 12x 60 12x 12 60 12 1x 5 x 5 The solution is 5. ✔ True b. To obtain a coefficient of 1 for the w-term, divide both sides by 8. Simplify. Check: 48w 8w 48 8162 48 48 48 8w 48 8 8w 8 6 1w 6 w The solution is 6. ✔ True c. Note that is equivalent to x 8 x 1 x. To obtain a coefficient of 1 for the x-term, divide by 1 . Check: 1x 8 1x 1 8 1 x 8 x 8 182 8 The solution is 8. 8 8 ✔ True TIP: The quotient of a nonzero real number and itself is always 1. For example: 5 5 3.5 3.5 1 1 Skill Practice Solve the equations. 12. 4x 20 13. 100 4p 14. y 11 Classroom Examples: p. 130, Exercises 38 and 50 TIP: In Example 4(c), we could also have multiplied both sides by 1 to create a coefficient of 1 on the x-term. x 8 1121x2 1128 x 8 Answers 12. 5 13. 25 14. 11
miller_introductory_algebra_3e_ch1_3
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