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

GOAL:

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

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

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

YOU TRY IT: What are the solutions to 3( t + 1) – 4t ≥ -1? linear_inequalities/inequalities/v/multi-step- inequalities-2

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

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?

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

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?

SOLUTION: Since the fence will go around the garden, we use: At most 42 ft. of fence Width on picture = 12 ft

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

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

VIDEOS: Inequalities ar_inequalities/inequalities/v/multi-step- inequalities-2 ar_inequalities/inequalities/v/multi-step- inequalities

CLASSWORK: Page Problems: As many as needed to master the concept.