Section 2.1 Addition, Subtraction, Multiplication, and Division Properties of Equality 105 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 of 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 set is {5}. ✔ True b. To obtain a coefficient of 1 for the w-term, divide both sides by 8. Simplify. Check: 48 8w 48 8162 48 48 48 8w 48 8 8w 8 6 1w 6 w The solution set 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 8 8 The solution set is {8}. ✔ True Skill Practice Solve the equations. 7. 4x 20 8. 100 4p 9. y 11 TIP: The quotient of a nonzero real number and itself is always 1. For example: 5 5 3.5 3.5 1 1 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 7. {5} 8. {25} 9. {11}
miller_beginning_intermediate_algebra_4e_ch1_3
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