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Warm Up

Solve Inequalities Using Addition and Subtraction. Warm Up. Lesson Presentation. Lesson Quiz. ANSWER. 12 x  60; no. Warm-Up. 1. Is – 9 a solution of a + 7 = – 2 ?. yes. ANSWER. 2. Solve the equation h + 12 = – 8. ANSWER. – 20.

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Warm Up

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  1. Solve Inequalities Using Addition and Subtraction Warm Up Lesson Presentation Lesson Quiz

  2. ANSWER 12x 60; no Warm-Up 1. Is –9 a solution of a + 7 =–2? yes ANSWER 2. Solve the equationh + 12 = –8. ANSWER –20 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?

  3. Example 1 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 Trepresent a temperature (in degrees Fahrenheit) in the United States. The value of Tmust be less than or equal to 134. So, an inequality is T 134.

  4. ANSWER x –129F Guided Practice 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 the Antarctica.

  5. a. 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. Example 2 Write an inequality represented by the graph. SOLUTION

  6. b. 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. Example 2 SOLUTION

  7. ANSWER ANSWER x<8 x –2.5 Guided Practice Write an inequality represented by the graph.

  8. Solve x – 5 > –3.5.Graph your solution. ANSWER The solutions are all real numbers greater than 1.5. Check by substituting a number greater than 1.5 for xin the original inequality. Example 3 x – 5 > –3.5 Write original inequality. x – 5 +5> –3.5 +5 Add 5 to each side. x > 1.5 Simplify.

  9. ? 6– 5 > –3.5 1> –3.5 Example 3 CHECK x– 5 > –3.5 Write original inequality. Substitute 6 for x. Solution checks.

  10. 1 1 2 2 ANSWER p < 4.2 ANSWER ANSWER x  12 m  6. –1 m – – Guided Practice Solve the inequality. Graph your solution. 4. x – 9  3 5. p – 9.2 < –5

  11. ANSWER You can rewrite2 x asx  2. The solutions are all real numbers less than or equal to 2. Example 4 Solve 9  x+ 7. Graph your solution. 9x+ 7 Write original inequality. 9– 7 x+ 7 – 7 Subtract 7 from each side. 2 x Simplify.

  12. ANSWER y> 0.5 Guided Practice 7. Solve y+ 5.5 > 6. Graph your solution.

  13. Example 5 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 weightsw(in pounds) that you can add to the bag. SOLUTION Write a verbal model. Then write and solve an inequality. 16.8 + w 50

  14. ANSWER You can add no more than33.2pounds. Example 5 Write inequality. 16.8 + w 50 16.8 + w –16.8 50 –16.8 Subtract 16.8 from each side. w  33.2 Simplify.

  15. w  20.9 lb ANSWER Guided Practice 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.

  16. ANSWER all real numbers less than 1 ANSWER all real numbers greater than or equal to –2 2. k – 6 < –5 Lesson Quiz Solve the inequality. Graph your solution. 1. s + 0.5  –1.5

  17. 3. 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 ofremaining tickets t the box office can sell. Lesson Quiz ANSWER t + 284  625; t 341; no more than 341 tickets.

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