188 Chapter 2 Linear Equations and Inequalities in One Variable 3. The statement “The sum of three times a number and 6 is the same as 4 less than the number.” can be written as a. 3(n + 6) = n - 4 b. 3(n + 6) = 4 - n c. 3n + 6 = n - 4 d. 3n + 6 = 4 - n 4. The equation that can be solved by subtracting 3 from each side is a. 3x = 21 b. 4 = 3 + x c. x - 3 = 5 d. 1 3 x = 4 5. In the Korean and Vietnam Wars, the United States lost a total of approximately 112,499 people. There were about 4007 fewer deaths in the Korean War than in the Vietnam War. How many U.S. deaths were there in each of these wars? If x represents the number of deaths in the Vietnam War, a. write an equation that can be used to solve this problem. b. solve the equation and explain the answer. Solve each equation. Write each solution in a solution set. 6. 7x - 3(2x + 1) = 0 7. 4(x + 3) = 5(2 - x) 8. 3 - x = -7 9. 3 2 b = 9 10. 4 + 3(2x - 5) = 7x + 6 - 2x 11. y 6 + 1 2 = 7 6 12. - 1 5 (x - 5) = 2 5 (x + 10) 13. 0.05x + 0.03(10,000 - x) = 440 14. 9y - 3(4y + 2) = 2y - 4 - 5y - 2 15. -2(b - 5) = 4(b + 1) - 6b 16. Solve the equation 4x + 3y = -12 for y. 17. Evaluate the formula C = 5 9 (F - 32) if F = 598. 18. Explain how solving linear equations and solving linear inequalities are the same. Explain how they are different. 19. The graph of -4 ≥ x can be represented as a. –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 b. –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 c. –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 d. –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 20. The interval notation for the following graph is –2 –1 0 1 2 3 4 5 6 7 8 a. (-∞, 3) b. (3, -∞) c. (∞, 3) d. (3, ∞) Solve each inequality. Graph the solution set. Write the solution in interval notation and set-builder notation. 21. 4x - 5(x - 2) ≥ -3 22. 2 3 (x - 1) < x + 4 3 Define a variable to represent the unknown quantity. Write an equation (or inequality) that represents each situation. Solve the equation and answer the question in a complete sentence. 23. A taxicab authority in Nevada has set standard fares and fees. To pick up a passenger, the cab company charges a fee of $3.30. For each mile driven, there is a charge of $2.40. a. If you have at most $75, how d far could you travel in the cab? Round your answer to the nearest tenth. b. The distance from your hotel to the Hoover Dam is 40.8 mi. Do you have enough money to travel there by taxicab? 24. The measure of the complement of an angle is 6° less than three times the measure of the angle. Find the measure of the angle. 25. The final grade in Joann’s math class is based upon a weighted average. Tests count as 50%, quizzes count as 15%, homework counts as 10%, and the final exam counts as 25%. If she has a test average of 84, a quiz average of 86, and a homework average of 100, what does she need on the final exam to have at least an 80 for her final grade? 26. Find the value of a and the measures of the vertical angles shown. 2(a + 10) + 5 3(a – 15) 27. Two of the angles in a triangle have equal measure. The third angle is 20 less than six times the measure of the two equal angles. Find the measure of each angle in the triangle. 28. An architect designs a circular stadium. If the footprint of the stadium has a perimeter of 180π ft, what is the area of the footprint of the stadium? Use 3.14 for the value of π. Round your answer to the nearest integer. 29. David has $3000 to invest. He invests part of the money in a savings account that earns 4% annual interest and the remaining amount in a CD that earns 6% annual interest. If he earns $164 in interest in 1 yr, how much money did he invest in each account? 30. A department store advertises that they donate 5% of their weekly profit to various charities. Their donation is approximately $3 million each week. What is the department store’s weekly profit? 31. Dr. Cleves is a pharmacist who needs a 15% glycerol solution. He has 10 mL of a 50% glycerol solution. How much water does he need to mix with the 10 mL of the 50% solution to obtain a solution that is 15% glycerol? Round to the nearest tenth. 32. The sum of the two smallest of three consecutive odd integers is the same as one less than three times the
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