Post on 12-Feb-2016
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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.
http://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/multi-step-inequalities
SOLUTION:9 + 4t > 21
Given 4t > 21 - 9
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 9 + 16 > 21 25 > 21 25 > 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?
http://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/multi-step-inequalities-2
SOLUTION:3( t + 1) – 4t ≥ -1 Given 3t + 3 - 4t ≥ -1
Distributive property
- t ≥ -1 -3 Add like terms
- t ≥ - 4
3 - 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%
Average
At least ≥
45% + x
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.
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:
≤ 42 At most 42 ft. of fence
Perimeter =
Width on picture = 12 ft
≤ 42 ≤ 42
≤ 42 - 24≤ 18≤ 9
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
https://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/multi-step-inequalities-2
https://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/multi-step-inequalities
CLASSWORK:
Page 189-192
Problems: As many as needed to master the
concept.