66 Chapter 2 Linear Equations and Inequalities in One Variable One of the first applications we will solve deals with consecutive integers. Consecutive means “successive” or “following one after another without interruption.” So, consecutive integers are integers that follow one another. Some examples are listed in the table. Specific Example Variable Representation Consecutive integers 4 5 6 +1 +1 x, x + 1, x + 2, . . . Consecutive even integers 10 12 14 +2 +2 x, x + 2, x + 4, . . . Consecutive odd integers 11 13 15 +2 +2 x, x + 2, x + 4, . . . Note: Consecutive odd and consecutive even integers are represented in the same way since the difference between these types of integers is 2 units. The value of x determines the numbers that will be generated from the expressions x + 2, x + 4, . . . . Objective 1 Examples Translate each problem into a linear equation and solve the problem. 1a. The sum of two consecutive integers is -9. Find the numbers. Solution 1a. What is unknown? Two consecutive integers are unknown. Let x represent one integer. The next integer is x + 1. What is given? The sum of the consecutive integers is 9. First integer plus second integer is -9. x + (x + 1)=-9 Express the relationship. 2x + 1=-9 Combine like terms. 2x + 1 - 1=-9 - 1 Subtract 1 from each side. 2x=-10 Simplify. 2x = -10 2 2 Divide each side by 2. x=-5 Simplify. One integer is -5. The other integer is x + 1=-5 + 1=-4. So, the numbers -4 and -5 are consecutive integers whose sum is -9. 1b. When the quotient of a number and 2 is subtracted from the number, the result is 6. Find the number. Solution 1b. What is unknown? A number is unknown. Let x represent the number. What is given? The quotient of a number and 2, subtracted from the number, is 6. A number less the quotient of the number and 2 is 6. x - x 2 = 6 Express the relationship. 2¢x - x 2 ≤ = 2(6) Multiply each side by 2. 2x - x = 12 Apply the distributive property and simplify. x = 12 Combine like terms. Since 12 checks in the equation, the number is 12.
hendricks_intermediate_algebra_1e_ch1_3
To see the actual publication please follow the link above