1. ALGEBRA 1 Lesson 3-5 Warm-Up

2. ALGEBRA 1 Lesson 3-5 Warm-Up

3. ALGEBRA 1 “Compound Inequalities” (3-5) (3-1) What is a compound inequality? Compound Inequality: two inequalities that are joined by the word and or the word or - A compound inequality joined by the word and means any number that makes both inequalities true. Example: x ≥ 5 and x ≤ 7 means “x is greater than or equal to -5 and less than or equal to 7”. It can also be written as -5 ≤ x ≤ 7 which means “x is between -5 and 7 inclusive (including those two values)”

4. ALGEBRA 1 Write a compound inequality that represents 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 less than 31, but greater than 25. n 25 25 < n < 31 Compound Inequalities LESSON 3-5 Additional Examples

5. ALGEBRA 1 “Compound Inequalities” (3-5) (3-1) How do you solve a compound inequality in which there are three parts (two inequality signs) joining the inequalities with “and”? Method 1: You can solve a compound inequality by splitting it up into two inequalities joined by and. Then, isolate the variable for each inequality. Example: Solve -4  r – 5 ≤ -1. -4  r - 5 and r – 5 ≤ -1 4 + 5  r - 5 + 5 and r – 5 + 5 ≤ -1 + 5 Add 5 to both inequalities. 1  r and r ≤ -4Simplify 1  r ≤ 4 Combine the inequalities Method 2: You can solve a compound inequality by isolating the variable by working on all three parts at the same time. Example: Solve -4  r – 5 ≤ -1. Graph the result. -4  r – 5 ≤ -1 -4 + 5  r – 5 + 5 ≤ -1 + 5Add 5 to all three parts of the inequality. 1  r ≤ 4 Simplify

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

7. ALGEBRA 1 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? Words:the average which is less than or equal to is less than or equal to 8590 Equation:8590 < 83 + 87 + g 3 g < Compound Inequalities LESSON 3-5 Additional Examples

8. ALGEBRA 1 (continued) 85 < 83 + 87 + g 3 < 90 << 255170 + g270Simplify. << 255 – 170170 + g – 170270 – 170Subtract 170. << 85g100Simplify. The third test grade must be between 85 and 100, inclusive. Compound Inequalities LESSON 3-5 Additional Examples Multiply by 3. 3(85) << 3(90) 83 + 87 + g 3 3

9. ALGEBRA 1 “Compound Inequalities” (3-5) (3-1) How do you solve a compound inequality in which two inequalities are joined by the word “or”? A compound inequality joined by the word or means any number that makes either inequality true. Example: -5 is a solution to the following compound inequality, because it is a solution to one of the inequalities (x < -3)

10. ALGEBRA 1 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 < 7 or a 65; because age cannot be negative, a ≥ 0. > Compound Inequalities LESSON 3-5 Additional Examples

11. ALGEBRA 1 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 < 1 x < –3x > 1 or Compound Inequalities LESSON 3-5 Additional Examples

12. ALGEBRA 1 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 LESSON 3-5 Lesson Quiz