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3.4 Solving Multi-Step inequalities:

Solution of an Inequality: Any number that makes the inequality true. . 3.4 Solving Multi-Step inequalities:. Inverse Operations: Operations that undo another operation. . Isolate: The use of inverse operations used to leave a variable by itself. . GOAL:. Multi-Step inequalities:.

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3.4 Solving Multi-Step inequalities:

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  1. Solution of an Inequality: Any number that makes the inequality true. 3.4 Solving Multi-Step inequalities: Inverse Operations: Operations that undo another operation. Isolate: The use of inverse operations used to leave a variable by itself.

  2. GOAL:

  3. Multi-Step inequalities: Just like the equations, we can isolate a variable in an inequality by using inverse operations. Ex: What are the solutions to 9 + 4t > 21 Check the solutions. http://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/multi-step-inequalities

  4. SOLUTION: 9 + 4t > 21 Given 4t > 21 - 9 Inverse of addition 4t > 12 > Inverse of multiplication t > 3  interval: (3, ∞)

  5. CHECK: 9 + 4t > 21 t > 3, we cannot use 3 but 4 and on… 9+ 4(4) > 21 9 + 16 > 21 25 > 21 25 > 21  TRUE Remember: sign switches direction when dividing or multiplying by a negative number.

  6. YOU TRY IT: What are the solutions to 3( t + 1) – 4t ≥ -1? http://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/multi-step-inequalities-2

  7. SOLUTION: 3( t + 1) – 4t ≥ -1 Given 3t + 3 - 4t ≥ -1 Distributive property 3 - t ≥ -1 Add like terms - t≥ -1 -3 Inverse of addition - t ≥ - 4 Add like terms ÷ by -1, Sign switches t ≤ 4 (-∞,4] Interval

  8. Real-World: You have taken a quiz and got 45%. You are about to take another quiz next week. If you want to pass the portion of quizzes in the class you must get an average of at least 70%. What is the minimum percentage you must get on the next quiz?

  9. Real-World: (SOLUTION) Quiz 1 = 45% Quiz 2 = x% Average  45% + x At least  ≥ x Thus in order for you to get an average of 70% in your quizzes, you must get at least 95% on the second quiz.

  10. Real-World: In a community garden, you want to plant and fence in a vegetable garden that is adjacent to your friend’s garden. You have at most 42 ft. of fence. What are the possible lengths of your garden?

  11. Since the fence will go around the garden, we use: SOLUTION: Perimeter = At most 42 ft. of fence ≤ 42 ≤ 42 Width on picture = 12ft ≤ 42 ≤ 42 - 24 ≤ 18 ≤ 9

  12. WRITING SET AND INTERVAL NOTATION: Always isolate variable, graph and write interval: x ≤ 0 Set Notation: { x| x ≤ 0}Interval Notation: (-∞, 0] x ≥ 2 Set Notation: { x| x ≥ 2}Interval Notation: [2, ∞)

  13. WRITING SET AND INTERVAL NOTATION: Always isolate variable, graph and write interval: x < -1 Set Notation: { x| x < -1}Interval Notation: (-∞, -1) x > 1 Set Notation: { x| x > 1}Interval Notation: (1,∞)

  14. VIDEOS: Inequalities https://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/multi-step-inequalities https://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/multi-step-inequalities-2

  15. CLASSWORK:Page 189-192 Problems: As many as needed to master the concept.

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