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Warm-Up Exercises 1. Is –9 a solution of a + 7 = –2? ANSWER yes 2. Solve the equation h + 12 = –8. ANSWER –20 Warm-Up Exercises 3. Write an inequality that describes the number of CDs you can buy for $12 each if you have no more than $60 to spend. Can you buy 6 CDs? ANSWER 12x ≤ 60; no Warm-Up1Exercises EXAMPLE Write and graph an inequality Death Valley The highest temperature recorded in the United States was 134°F at Death Valley, California, in 1913. Use only this fact to write and graph an inequality that describes the temperatures in the United States. SOLUTION Let T represent a temperature (in degrees Fahrenheit) in the United States. The value of T must be less than or equal to 134. So, an inequality is T ≤ 134. Warm-Up2Exercises EXAMPLE Write inequalities from graphs Write an inequality represented by the graph. a. SOLUTION a. The open circle means that –6.5 is not a solution of the inequality. Because the arrow points to the right, all numbers greater than –6.5 are solutions. ANSWER An inequality represented by the graph is x > –6.5. Warm-Up2Exercises EXAMPLE Write inequalities from graphs b. SOLUTION b. The closed circle means that 4 is a solution of the inequality. Because the arrow points to the left, all numbers less than 4 are solutions. ANSWER An inequality represented by the graph is x ≤ 4. Warm-Up Exercises GUIDED PRACTICE for Example 1 and 2 Write an inequality represented by the graph. ANSWER x ≥ –2.5 Warm-Up3Exercises EXAMPLE Solve an inequality using addition Solve x – 5 > –3.5. Graph your solution. x – 5 > –3.5 x – 5 + 5 > –3.5 + 5 x > 1.5 Write original inequality. Add 5 to each side. Simplify. ANSWER The solutions are all real numbers greater than 1.5. Check by substituting a number greater than 1.5 for x in the original inequality. Warm-Up3Exercises EXAMPLE Solve an inequality using addition CHECK x – 5 > –3.5 ? 6 – 5 > –3.5 1 > –3.5 Write original inequality. Substitute 6 for x. Solution checks. Warm-Up Exercises GUIDED PRACTICE for Example 3 Solve the inequality. Graph your solution. 4. x – 9 ≤ 3 ANSWER x ≤ 12 Warm-Up Exercises GUIDED PRACTICE for Example 3 Solve the inequality. Graph your solution. 5. p – 9.2 < –5 ANSWER p < 4.2 Warm-Up Exercises GUIDED PRACTICE for Example 3 Solve the inequality. Graph your solution. 6. –1 ≥ m – 1 2 ANSWER m≤ –1 2 EXAMPLE Warm-Up5Exercises Solve a real-world problem LUGGAGE WEIGHTS You are checking a bag at an airport. Bags can weigh no more than 50 pounds. Your bag weighs 16.8 pounds. Find the possible weights w (in pounds) that you can add to the bag. SOLUTION Write a verbal model. Then write and solve an inequality. 16.8 + w ≤ 50 EXAMPLE Warm-Up5Exercises Solve a real-world problem 16.8 + w ≤ 50 16.8 + w – 16.8 ≤ 50 – 16.8 w ≤ 33.2 Write inequality. Subtract 16.8 from each side. Simplify. ANSWER You can add no more than 33.2 pounds. Warm-Up Exercises GUIDED PRACTICE 7. for Examples 4 and 5 Solve y + 5.5 > 6. Graph your solution. ANSWER y > 0.5 Warm-Up Exercises GUIDED PRACTICE for Examples 4 and 5 8. WHAT IF? In Example 5, suppose your bag weighs 29.1 pounds. Find the possible weights (in pounds) that you can add to the bag. ANSWER w ≤ 20.9 lb Warm-Up Exercises Warm-up: Page 296 #1-19 all Homework: Page 301 #3-28 all Warm-Up Example 1 Exercises Antarctica The lowest temperature recorded in Antarctica was –129°F at the Russian Vostok station in 1983. Use only this fact to write and graph an inequality that describes the temperatures in Antarctica. ANSWER x ≥ –129°F Warm-Up Exercises GUIDED PRACTICE Write an inequality represented by the graph. ANSWER x<8 Daily Homework Quiz Warm-Up Exercises Solve the inequality. Graph your solution. 3. s + 0.5 ≥ –1.5 ANSWER all real numbers greater than or equal to –2 4. k – 6 < –5 ANSWER all real numbers less than 1 EXAMPLE Warm-Up5Exercises Solve an inequality using subtraction Solve 9 ≥ x + 7. Graph your solution. 9≥x+7 9–7≥x+7–7 2≥x Write original inequality. Subtract 7 from each side. Simplify. ANSWER You can rewrite 2 ≥ x as x ≤ 2. The solutions are all real numbers less than or equal to 2. Daily Homework Quiz Warm-Up Exercises 6. A theater can seat at most 625 people. The box office has sold tickets for 284 seats. Write and solve an inequality to find the possible numbers of remaining tickets t the box office can sell. ANSWER t + 284 ≤ 625; t ≤ 341; no more than 341 tickets.