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hendricks_beginning_algebra_1e_ch1_3

Section 2.3 The Multiplication Property of Equality 119 Note that consecutive odd and consecutive even integers are represented in the same way since the difference between these types of integers is two units. The value of x determines the numbers that will be generated from the expressions x + 2 and x + 4. If x = 15, then x + 2 = 15 + 2 = 17 and x + 4 = 15 + 4 = 19. So, the numbers generated are 15, 17, and 19. If x = 22, then x + 2 = 22 + 2 = 24 and x + 4 = 22 + 4 = 26. So, the numbers generated are 22, 24, and 26. �� ������������������������ ������������������ Write an equation that represents each problem. Solve the equation and explain the answer a complete sentence. 4a. The sum of two consecutive integers is -21. Find the integers. 4b. Three times the smallest of three consecutive odd integers is 17 more than the sum of the other two integers. Find the integers. Solutions 4a. What is unknown? Two consecutive integers are unknown. Let x and x + 1 represent the two integers. What is known? The sum of the two integers is -21. We use this statement to write the equation. The sum of the two integers is -21. x + (x + 1) = -21 Express the relationship. 2x + 1=-21 Combine like terms. 2x + 1 - 1=-21 - 1 Subtract 1 from each side. 2x=-22 Simplify. 2x 2 = -22 2 Divide each side by 2. x=-11 Simplify. Since x = -11, the integers are -11 and -11 + 1 = -10. 4b. What is unknown? Three consecutive odd integers are unknown. Let x, x + 2, and x + 4 represent the three odd integers. What is known? Three times the smallest of three consecutive odd integers is 17 more than the sum of the other two integers. We use this statement to obtain the equation. Three times the smallest of three consecutive odd integers is 17 more than the sum of the other two integers 3(x) = (x + 2) + (x + 4) + 17 Express the relationship. 3x = 2x + 23 Combine like terms. 3x - 2x = 2x + 23 - 2x Subtract 2x from each side. x = 23 Simplify. Since x = 23, the integers are 23, 23 + 2 = 25, and 23 + 4 = 27. Student Check 4 Write an equation that represents each problem. Solve the equation and explain the answer using a complete sentence. a. The sum of two consecutive integers is -137. Find the integers. b. Five times the smallest of three consecutive even integers is two more than twice the sum of the other two integers. Find the integers.


hendricks_beginning_algebra_1e_ch1_3
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