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.