58 Chapter 1 Linear Equations and Inequalities in One Variable Translating and Solving a Linear Equation Example 1 The sum of two numbers is 39. One number is 3 less than twice the other.What are the numbers? Solution: Step 1: Read the problem carefully. Step 2: Let x represent one number. Let 2x 3 represent the other number. Step 3: (One number) (other number) 39 Step 4: Replace the verbal model with a mathematical equation. (One number) (other number) 39 x (2x 3) 39 Answer 1. The numbers are 10 and 35. Step 5: Solve for x. x 12x 32 39 3x 3 39 3x 42 3x 3 42 3 x 14 Step 6: Interpret your results. Refer back to step 2. One number is x: 14 The other number is 2x 3: 2(14) 3 25 Answer: The numbers are 14 and 25. Skill Practice 1. One number is 5 more than 3 times another number.The sum of the numbers is 45. Find the numbers. 2. Applications Involving Consecutive Integers The word consecutive means “following one after the other in order.” • The numbers 2, 1, 0, 1, 2, and so on are examples of consecutive integers. Notice that two consecutive integers differ by 1. Therefore, if x represents an integer, then x 1 represents the next consecutive integer. • The numbers 2, 4, 6, 8, and so on are consecutive even integers. Consecutive even integers differ by 2. Therefore, if x represents an even integer, then x 2 represents the next consecutive even integer. • The numbers 15, 17, 19, and so on are consecutive odd integers. Consecutive odd integers also differ by 2. Therefore, if x represents an odd integer, then x 2 represents the next consecutive odd integer.
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