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ALGEBRA 1 LESSON 10-4 (For help, go to Lessons 1-1 and 3-1.) Graph each pair of inequalities on one number line. 1.c 12 Use the given value of the variable to evaluate each expression. 4.3n – 6; 45.7 – 2b; 5 6. ; 177. ; 9 > < > < 12 + 13 + y 3 2d – 3 5 Compound Inequalities 10-4

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ALGEBRA 1 LESSON 10-4 1. c < 8; c 10 2. t –2; t –5 3. m 7; m > 12 4. 3n – 6 for n = 4: 3(4) – 6 = 12 – 6 = 6 5. 7 – 2b for b = 5: 7 – 2(5) = 7 – 10 = –3 6. for y = 17: = = 14 7. for d = 9: = = = 3 > >< < 12 + 13 + y 3 2d – 3 5 12 + 13 + 17 3 42 3 2(9) – 3 5 18 – 3 5 15 5 Compound Inequalities Solutions 10-4

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ALGEBRA 1 LESSON 10-4 Write two compound inequalities that represent each situation. Graph the solutions. a. all real numbers that are at least –1 and at most 3. b –1 and b 3 –1 b 3 ><<< b. all real numbers that are at less than 31, but greater than 25. 31 > n and n > 25 31 > n > 25 Compound Inequalities 10-4

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Solve 5 > 5 – f > 2. Graph the solutions. ALGEBRA 1 LESSON 10-4 5 – f – 5 > 2 – 5 –f > –3 –3 –1 –f –1 < 5 – 5 > 5 – f – 5 0 > –f 0 –1 –f –1 < 5 – f > 25 > 5 – f and f < 30 < f and 0 < f < 3 Write the compound inequality as two inequalities joined by and. Compound Inequalities 10-4

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ALGEBRA 1 LESSON 10-4 Your test grades in science so far are 83 and 87. What possible grades g can you make on your next test to have an average between 85 and 90? Relate:the average which is less than or equal to is less than or equal to 8590 Write:8590 < 83 + 87 + g 3 g < Compound Inequalities 10-4

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ALGEBRA 1 LESSON 10-4 (continued) 85 < 83 + 87 + g 3 < 90 Multiply by 3. 3(85) << 3(90) 83 + 87 + g 3 3 ( ) << 255170 + g270Simplify. << 255 – 170170 + g – 170270 – 170Subtract 170. << 85g100Simplify. The third test grade must be between 85 and 100, inclusive. Compound Inequalities 10-4

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ALGEBRA 1 LESSON 10-4 Write an inequality that represents each situation. Graph the solutions. a. all real numbers that are less than 0 or greater than 3. n 3 b. Discounted tickets are available to children under 7 years old or to adults 65 and older. a 0. > Compound Inequalities 10-4

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ALGEBRA 1 LESSON 10-4 Solve the compound inequality 3x + 2 < –7 or –4x + 5 < 1. Graph the solution. 3x + 2 – 2 < –7 – 2 3x < –9 < 3x33x3 –9 3 –4x + 5 – 5 < 1 – 5 –4x < –4 > –4x –4 3x + 2 < –7–4x + 5 < 1or x < –3x > 1 or Compound Inequalities 10-4

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ALGEBRA 1 LESSON 10-4 1.Write two compound inequalities that represent the given situation. Graph the solution. all real numbers that are at least 2 and at most 5 2.Write an inequality that represents the given situation. Graph the solution. all real numbers that are less than –3 or greater than –1 3.Solve –2 2x – 4 < 6. Graph the solution. 4.Solve 3x – 2 < –8 or –2x + 5 3. Graph the solution. < < b 2 and b 5, 2 b 5 ><<< n –1 1 x < 5 < > x < –2 or x 1 Compound Inequalities 10-4

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