Section 1.2 Applications of Linear Equations in One Variable 65 Section 1.2 Practice Exercises Study Skills Exercise After doing a section of homework, check the odd-numbered answers in the back of the text. Choose a method to identify the exercises that gave you trouble (i.e., circle the number or put a star by the number). List some reasons why it is important to label these problems. Vocabulary and Key Concepts 1. a. Integers that follow one after the other without “gaps” are called integers. b. The integers 2, 0, 2, and 4 are examples of consecutive integers, and the integers 3,1, 1, and 3 are examples of consecutive integers. c. Two consecutive integers differ by , two consecutive odd integers differ by , and two consecutive even integers differ by . d. If x represents the smaller of two consecutive integers, then the expression represents the next greater consecutive integer. e. If x represents the smaller of two consecutive odd integers, then the expression represents the next greater consecutive odd integer. f. If x represents the smallest of three consecutive even integers, then the expressions and represent the next two greater consecutive even integers. g. Simple interest is interest computed on the principal invested or borrowed. Simple interest is computed as I where P is the principal, r is the annual rate, and t is the time in years. h. If $5000 is borrowed at 6.5% simple interest for 4 yr, then the amount of simple interest is . i. Suppose that 12% of a solution is acid by volume and the remaining 88% is water.Then the amount of acid in a 4-L container of solution is .The amount of acid in a container containing x 8 liters of solution is represented by the expression . j. If d rt,then r and t . Review Exercises 2. Identify the smallest positive integer that could be used to clear fractions in the equation. For Exercises 3–8, solve the equations. 2 3 x 4 5 1 1 6 x 3. 7a 2 11 4. 2z 615 5. 41x 32 7 19 3 8 3 4 3 2 6. 31y 52 4 1 7. 8. 1 4 2x 5 p p For the remaining exercises, follow the steps outlined in the Problem-Solving Flowchart found on page 57. Concept 1: Introduction to Problem Solving 9. If x represents a number, write an expression for 5 more than the number. 10. If n represents a number, write an expression for 10 less than the number.
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