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8 > x + 10. 1. 2. 6  2 x – 4. Solve the inequality. all real numbers less than – 2. ANSWER. ANSWER. all real numbers greater than or equal to 5. 3. You estimate you can read at least 8 history text pages per day. What are the possible numbers of

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  1. 8 > x + 10 1. 2. 6  2x– 4 Solve the inequality. all real numbers less than–2 ANSWER ANSWER all real numbers greater than or equal to 5

  2. 3. You estimate you can read at least 8 history text pages per day. What are the possible numbers of days it will take you to read at most 118 pages? at most 15 days ANSWER

  3. a. All real numbers that are greater than –2and less than 3 Graph: b. All real numbers that are less than 0or greater than or equal to 2 Graph: EXAMPLE 1 Write and graph compound inequalities Translate the verbal phrase into an inequality. Then graph the inequality. Inequality: –2 < x < 3 x < 0 or x  2 Inequality:

  4. 1. All real numbers that are less than –1or greater than or equal to 4 All real numbers that are greater than orequal To –3and less than 5 2. for Example 1 GUIDED PRACTICE Translate the verbal phrase into an inequality. Then graph the inequality. Inequality: x < –1 or x  4 = –3 x < 5 x  –3andx < 5 Inequality:

  5. EXAMPLE 2 Write and graph a real-world compound inequality CAMERA CARS A crane sits on top of a camera car and faces toward the front. The crane’s maximum height and minimum height above the ground are shown. Write and graph a compound inequality that describes the possible heights of the crane.

  6. EXAMPLE 2 Write and graph a real-world compound inequality SOLUTION Let hrepresent the height (in feet) of the crane. All possible heights are greater than or equal to 4 feet and less than or equal to 18 feet. So, the inequality is 4 h  18.

  7. 2 < x + 5 x + 5 < 9 and 2 – 5< x + 5 – 5 and x + 5 – 5< 9 – 5 and x < 4 –3 < x EXAMPLE 3 Solve a compound inequality with and Solve 2 < x + 5 < 9. Graph your solution. SOLUTION Separate the compound inequality into two inequalities. Then solve each inequality separately. Write two inequalities. Subtract 5 from each side. Simplify. The compound inequality can be written as –3 < x < 4.

  8. Graph: EXAMPLE 3 Solve a compound inequality with and ANSWER The solutions are all real numbers greater than –3and less than 4.

  9. ANSWER c < –3 or c > 4.5 An investor buys shares of a stock and will sell them if the change c in value from the purchase price of a share is less than –$3.00 or greater than $4.50. Write and graph a compound inequality that describes the changes in value for which the shares will be sold. 3. for Example 2 and 3 GUIDED PRACTICE Investing

  10. 4. –7 < x – 5 < 4 ANSWER –2 < x < 9 9 Graph: – 6 – 4 – 2 0 2 4 6 8 10 EXAMPLE 3 for Example 2 and 3 GUIDED PRACTICE Solve a compound inequality with and Solve the inequality. Graph your solution.

  11. 5. 10  2y + 4  24 3 y  10 ANSWER 3 Graph: 0 2 4 6 8 10 12 for Example 2 and 3 GUIDED PRACTICE Solve the inequality. Graph your solution.

  12. 6. –7 < –z – 1< 3 ANSWER –4 < z < 6 EXAMPLE 3 for Example 2 and 3 GUIDED PRACTICE Solve a compound inequality with and Solve the inequality. Graph your solution.

  13. EXAMPLE 4 Solve a compound inequality with and Solve –5  –x – 3  2. Graph your solution. –5  –x – 3  2 Write original inequality. –5 +3–x – 3 + 3 2 + 3 Add 3 to each expression. –2  –x  5 Simplify. –1(–2) –1(–x) –1(5) Multiply each expression by –1 and reverse both inequality symbols. 2 x –5 Simplify.

  14. ANSWER The solutions are all real numbers greater than or equal to –5and less than or equal to 2. EXAMPLE 4 Solve a compound inequality with and –5 x  2 Rewrite in the form a x b.

  15. or 2x + 3 < 9 3x – 6 > 12 or 3x – 6 + 6> 12 + 6 2x + 3 – 3< 9 – 3 or 2x < 6 3x > 18 EXAMPLE 5 Solve a compound inequality with or Solve 2x + 3 < 9 or 3x – 6 > 12. Graph your solution. SOLUTION Solve the two inequalities separately. Write original inequality. Addition or Subtraction property of inequality Simplify.

  16. 2x 3x < or 3 2 > 18 or x > 6 x < 3 3 6 ANSWER 2 The solutions are all real numbers less than 3or greater than 6. EXAMPLE 5 Solve a compound inequality with or Division property of inequality Simplify.

  17. –6 <x < 7 ANSWER for Examples 4 and 5 GUIDED PRACTICE Solve the inequality. Graph your solution. 7. –14 < x – 8 < –1

  18. ANSWER 2 3 5 5 – t  for Examples 4 and 5 GUIDED PRACTICE Solve the inequality. Graph your solution. 8. –1  –5t + 2  4

  19. or 2h – 5 > 7 9. 3h + 1< – 5 h < –2 orh > 6 ANSWER for Examples 4 and 5 GUIDED PRACTICE Solve the inequality. Graph your solution.

  20. 10. 4c + 1  –3 or 5c – 3 > 17 c –1 or c > 4 ANSWER for Examples 4 and 5 GUIDED PRACTICE Solve the inequality. Graph your solution.

  21. EXAMPLE 6 Solve a multi-step problem Astronomy The Mars Exploration Rovers Opportunity and Spirit are robots that were sent to Mars in 2003 in order to gather geological data about the planet. The temperature at the landing sites of the robots can range from 100°C to 0°C. • Write a compound inequality that describes the possible temperatures (in degrees Fahrenheit) at a landing site. • Solve the inequality. Then graph your solution. • Identify three possible temperatures (in degrees Fahrenheit) at a landing site.

  22. Let Frepresent the temperature in degrees Fahrenheit, and let Crepresent the temperature in degrees Celsius. Use the formula C = (F – 32). 5 9 5 9 5 –100 0 (F – 32) Substitute (F – 32) for C. 9 EXAMPLE 6 Solve a multi-step problem SOLUTION STEP1 Write a compound inequality. Because the temperature at a landing site ranges from –100°C to 0°C, the lowest possible temperature is –100°C, and the highest possible temperature is 0°C. –100 C 0 Write inequality using C.

  23. –100 0 (F – 32) 9 Multiply each expression by . 5 5 9 EXAMPLE 6 Solve a multi-step problem STEP 2 Solve the inequality. Then graph your solution. Write inequality from Step 1. –180  (F – 32 )0 –148 F 32 Add 32 to each expression.

  24. EXAMPLE 6 Solve a multi-step problem STEP 3 Identify three possible temperatures. The temperature at a landing site is greater than or equal to –148°Fand less than or equal to 32°F. Three possible temperatures are –115°F, 15°F, and 32°F.

  25. 11. Mars has a maximum temperature of 7°C at the equator and a minimum temperature of –133°Cat the winter pole. 5 9 ANSWER –133 ≤ (F– 32) ≤ 27; 207.4 ≤ F ≤ 80.6 for Example 6 GUIDED PRACTICE • Write and solve a compound inequality that describes the possible temperatures (in degrees Fahrenheit) on Mars.

  26. ANSWER Sample answer: 100°F, 0°F, 25°F for Example 6 GUIDED PRACTICE • Graph your solution. Then identify three possible temperatures (in degrees Fahrenheit) on Mars.

  27. ANSWER all real numbers less than3or greaterthan4 2. Solve 3x + 2 > –7 and 4x – 1 < –5. Graph your solution. ANSWER all real numbers greater than –3and less than –1 Daily Homework Quiz 1. Solvex + 4 < 7 or 2x – 5 > 3. Graph your solution.

  28. 3. The smallest praying mantis is 0.4 inch in length. The largest is 6 inches. Write and graph a compound inequality that describes the possible lengths L of a praying mantis. ANSWER 0.4 L 6 < < – – Daily Homework Quiz

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