2 Warm-UpSolve the inequality.1.8 > x + 10ANSWERall real numbers less than –26 2x – 42.ANSWERall real numbers greater than or equal to 53.You estimate you can read at least 8 history textpages per day. What are the possible numbers ofday it will take you to read at most 118 pages?ANSWERat most 15 days
3 Example 1Translate the verbal phrase into an inequality. Thengraph the inequality.a.All real numbers that are greater than –2 and lessthan 3Inequality:–2 < x < 3Graph:b.All real numbers that are less than 0 or greater thanor equal to 2Inequality:x < 0 or x 2Graph:
4 Guided PracticeTranslate the verbal phrase into an inequality. Thengraph the inequality.All real numbers that are less than –1 or greater thanor equal to 41.Inequality:x < –1 or x 42.All real numbers that are greater than or equalTo –3 and less than 5Inequality:x –3 and x < 5= –3 x < 5
5 Example 2CAMERA CARSA 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 2SOLUTIONLet h represent 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 Guided PracticeInvestingAn 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.c < –3 or c > 4.5ANSWER
8 Solve 2 < x + 5 < 9. Graph your solution. Example 3Solve 2 < x + 5 < 9. Graph your solution.SOLUTIONSeparate the compound inequality into two inequalities. Then solve each inequality separately.2 < x + 5x + 5 < 9andWrite two inequalities.2 – 5 < x + 5 – 5x + 5 – 5 < 9 – 5andSubtract 5 from each side.–3 < xx < 4andSimplify.The compound inequality can be written as –3 < x < 4.
9 Example 3ANSWERThe solutions are all real numbers greater than –3 andless than 4.Graph:
10 Solve the inequality. Graph your solution. –7 < x – 5 < 4 4. Guided PracticeSolve the inequality. Graph your solution.–7 < x – 5 < 44.–2 < x < 9ANSWER– – –9Graph:10 2y + 4 245.3 y 10ANSWERGraph:3–7 < –z – 1 < 36.–4 < z < 6ANSWER
11 Solve –5 –x – 3 2. Graph your solution. Example 4Solve –5 –x – 3 2. Graph your solution.–5 –x – 3 2Write original inequality.–5 + 3 –x – 2 + 3Add 3 to each expression.–2 –x 5Simplify.–1(–2) –1(–x) –1(5)Multiply each expression by –1 and reverse both inequality symbols.2 x –5Simplify.–5 x 2Rewrite in the forma x b.
12 Example 4ANSWERThe solutions are all real numbers greater than or equal to –5 and less than or equal to 2.
13 Guided PracticeSolve the inequality. Graph your solution.7. –14 < x – 8 < –1–6 < x < 7ANSWER8. –1 –5t + 2 4– t 253ANSWER
14 Solve 2x + 3 < 9 or 3x – 6 > 12. Graph your solution. Example 5Solve 2x + 3 < 9 or 3x – 6 > 12. Graph your solution.SOLUTIONSolve the two inequalities separately.2x + 3 < 9or3x – 6 > 12Write originalinequality.2x + 3 – 3 < 9 – 3or3x – >Addition orSubtractionproperty ofinequality2x < 6or3x > 18Simplify.
15 The solutions are all real numbers less than 3 or greater than 6. Example 52x26<or3x318>Division property of inequalityx < 3orx > 6Simplify.ANSWERThe solutions are all real numbers less than 3 or greaterthan 6.
16 Guided PracticeSolve the inequality. Graph your solution.h + 1< – 5or2h – 5 > 7h < –2 or h > 6ANSWERc + 1 –3or5c – 3 > 17c –1 or c > 4ANSWER
17 Example 6AstronomyThe 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.
18 Celsius. Use the formula 5 9 C = (F – 32). Example 6SOLUTIONLet F represent the temperature in degrees Fahrenheit, and let C represent the temperature in degreesCelsius. Use the formula59C = (F – 32).STEP 1Write 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 0Write inequality using C.(F – 32)–100 059Substitute (F – 32) for C.95
19 Solve the inequality. Then graph your solution. Example 6STEP 2Solve the inequality. Then graph your solution.(F – 32)–100 059Write inequality from Step 1.Multiply each expression by59–180 (F – 32 ) 0–148 F 32Add 32 to each expression.
20 Example 6STEP 3Identify three possible temperatures.The temperature at a landing site is greater than or equal to –148°F and less than or equal to 32°F. Three possible temperatures are –115°F, 15°F, and 32°F.
21 Guided PracticeMars has a maximum temperature of 27°C at the equator and a minimum temperature of –133°C at the winter pole.11.• Write and solve a compound inequality that describes the possible temperatures (in degree Fahrenheit) on Mars.ANSWER–133 ≤ (F– 32) ≤ 27; 207.4 ≤ F ≤ 80.659• Graph your solution. Then identify three possible temperatures (in degrees Fahrenheit) on Mars.ANSWERSample answer: 100°F, 0°F, 25°F
22 Lesson Quiz1. Solve x + 4 < 7 or 2x – 5 > 3. Graph your solution.ANSWERall real numbers less than 3 or greater than 42.Solve 3x + 2 > –7 and 4x – 1 < –5. Graph your solution.ANSWERall real numbers greater than –3 and less than –1
23 Lesson QuizThe 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.3.ANSWERL 6<–