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To graph this inequality, draw a solid circle at draw an arrow extending to the left. and 1-5 Solving Inequalities Solve each inequality. Then graph the solution set on a number line. 15. 11. SOLUTION: SOLUTION: To graph this inequality, draw a solid circle at -3 and draw an arrow extending to the left. To graph this inequality, draw an open circle at 27 and draw an arrow extending to the left. 13. SOLUTION: 17. SOLUTION: To graph this inequality, draw a solid circle at draw an arrow extending to the left. and To graph this inequality, draw an open circle at 3 and draw an arrow extending to the left. 15. SOLUTION: 19. SOLUTION: To graph this inequality, draw an open circle at 27 and draw an arrow extending to the left. eSolutions Manual - Powered by Cognero 17. SOLUTION: Page 1 To graph this inequality, draw an open circle at 1 and draw an arrow extending to the left. To graph this inequality, draw an open circle at 3 and draw an arrow extending to the left. To graph this inequality, draw an open circle at 3 and draw an arrow extending to the left. 1-5 Solving Inequalities 19. SOLUTION: Define a variable and write an inequality for each problem. Then solve. 23. Twelve less than the product of three and a number is less than 21. SOLUTION: Let x be the unknown number. To graph this inequality, draw an open circle at 1 and draw an arrow extending to the left. 25. The difference of 5 times a number and 6 is greater than the number. SOLUTION: Let x be the unknown number. 21. SOLUTION: 27. HIKING Danielle can hike 3 miles in an hour, but she has to take a one-hour break for lunch and a one-hour break for dinner. If Danielle wants to hike at least 18 miles, solve to determine how many hours the hike should take. SOLUTION: To graph this inequality, draw an open circle at 3 and draw an arrow extending to the left. Define a variable and write an inequality for each problem. Then solve. 23. Twelve less than the product of three and a number is less than- 21. eSolutions Manual Powered by Cognero SOLUTION: Let x be the unknown number. Danielle has to hike for at least 8 hours. Page 2 Solve each inequality. Then graph the solution set on a number line. 29. and draw an arrow extending to the right. 1-5 Solving Inequalities 27. HIKING Danielle can hike 3 miles in an hour, but she has to take a one-hour break for lunch and a one-hour break for dinner. If Danielle wants to hike at least 18 miles, solve to determine how many hours the hike should take. 31. SOLUTION: SOLUTION: To graph this inequality, draw an open circle at 18.75 and draw an arrow extending to the right. Danielle has to hike for at least 8 hours. Solve each inequality. Then graph the solution set on a number line. 33. SOLUTION: 29. SOLUTION: To graph this inequality, draw an open circle at –4.5 and draw an arrow extending to the right. To graph this inequality, draw an open circle at and draw an arrow extending to the right. 35. SOLUTION: 31. SOLUTION: eSolutions Manualthis - Powered by Cognero To graph inequality, draw an open circle at 18.75 and draw an arrow extending to the right. Page 3 To graph this inequality, draw an open circle at –4.5 and draw an arrow extending to the right. To graph this inequality, draw an open circle at and draw an arrow extending to the right. 1-5 Solving Inequalities Solve each equation. Check your solutions. 35. 55. SOLUTION: SOLUTION: To graph this inequality, draw an open circle at and draw an arrow extending to the right. There appear to be two solutions, . Check: Substitute the values in the original equation. Solve each equation. Check your solutions. 55. SOLUTION: The solution set is 57. ASTRONOMY Pluto travels in a path that is not circular. Pluto’s farthest distance from the Sun is 4539 million miles, and its closest distance is 2756 million miles. Write an equation that can be solved to find the minimum and maximum distances from the Sun to Pluto. There appear to be two solutions, . . SOLUTION: Check: Substitute the values in the original equation. eSolutions Manual - Powered by Cognero Page 4 The solution set is 1-5 Solving Inequalities Substitute r = 891.5 and c = 3647.5 in the equation . . 57. ASTRONOMY Pluto travels in a path that is not circular. Pluto’s farthest distance from the Sun is 4539 million miles, and its closest distance is 2756 million miles. Write an equation that can be solved to find the minimum and maximum distances from the Sun to Pluto. SOLUTION: 59. GEOMETRY The formula for the surface area of a cylinder is . a. Use the Distributive Property to rewrite the formula by factoring out the greatest common factor of the two terms. b. Find the surface area for a cylinder with radius 3 centimeters and height 10 centimeters using both formulas. Leave the answer in terms of . c. Which formula do you prefer? Explain your reasoning. SOLUTION: a. The value of c is 4539 – 891.5 or 3647.5. Substitute r = 891.5 and c = 3647.5 in the equation . The GCF of the two terms is 2πr. 59. GEOMETRY The formula for the surface area of a cylinder is . a. Use the Distributive Property to rewrite the formula by factoring out the greatest common factor of the two terms. b. Find the surface area for a cylinder with radius 3 centimeters and height 10 centimeters using both formulas. Leave the answer in terms of . c. Which formula do you prefer? Explain your reasoning. b. Substitute r = 3 and h = 10 in the formula . SOLUTION: a. Substitute r = 3 and h = 10 in the formula The GCF of the two terms is 2πr. Therefore, the surface area of the cylinder is 78π 2 cm . b. Substitute r = 3 and h = 10 in the formula . c. Sample answer: The formula in part b is quicker. Solve each equation. Check your solutions. 61. SOLUTION: eSolutions Manual - Powered by Cognero Substitute r = 3 and h = 10 in the formula The solution set is . Page 5 Therefore, the surface area of the cylinder is 78π 2 cm . 1-5 Solving Inequalities c. Sample answer: The formula in part b is quicker. Solve each equation. Check your solutions. The solution set is . 65. 61. SOLUTION: SOLUTION: The solution set is . 63. SOLUTION: There appear to be two solutions, –6 and 2. Check: Substitute the values in the original equation. There appear to be two solutions, . Check: Substitute the values in the original equation. The solution set is . The solution set is . 65. SOLUTION: eSolutions Manual - Powered by Cognero Page 6