3.6 compound inequalities:
DESCRIPTION
Inverse Operations: Operations that undo another operation. 3.6 Compound inequalities:. Isolate: The use of inverse operations used to leave a variable by itself. Compound Inequalities: two distinct inequalities joined by the word and or the word or. GOAL:. Compound inequalities:. - PowerPoint PPT PresentationTRANSCRIPT
3.6 Compound inequalities:
Inverse Operations: Operations that undo another operation.
Isolate: The use of inverse operations used to leave a variable by itself.
Compound Inequalities: two distinct inequalities joined by the word and or the word or.
GOAL:
These inequalities have the following graphs when the word and is being used:
Compound inequalities:
Set Notation: {x|3 ≤ x ≤ 7}
Interval: [3, 7]
Compound inequalities:
Set Notation: {x| x < -2 or x ≥1}Interval: (-∞,-2)U[1, ∞)
These inequalities have the following graphs when the word or is being used:
WRITING Compound inequalities:We must be able to transform English sentences into math equations:
EX:What compound inequality
represents the phrase:
“ All real numbers that are greater than – 2 and less than or equal to 6”
SOLUTION:“ All real numbers that are greater than – 2 and less than or equal to 6”
All real numbers greater than -2 X > -2
andAll real numbers less than or equal to 6
X ≤ 6-2 < x ≤ 6
Set Notation: {x| -2 < x ≤ 6} Interval: (-2, 6]
YOU TRY IT:
What compound inequality represents the phrase:
“ All real numbers that are less than 0 or greater than 5”
SOLUTION: “ All real numbers that are less than 0 or greater than 5”
All real numbers less than 0 X < 0
orAll real numbers greater than 5 X > 5
x< 0, x > 5
Set Notation: {x| x < 0, x > 5} Interval: (-∞,0) U (5, ∞)
SOLVING Compound Inequalities:To solve inequalities we follow inverse operations just like we do to isolate a variable:
EX:What are the solutions of: - 2 ≤ 2m – 4 < -1
SOLUTION:- 2 ≤ 2m – 4 < -1 Given (and)
4 - 2 ≤ 2m <-1 + 4 Inverse of subt.
2 ≤ 2m < 3 ≤ m <
Like terms
1 ≤ m < 1.5
Inverse of mult.
Interval: [1, 1.5)
YOU TRY IT:
What are the solutions
to 3t + 2 < -7 or -4t + 5 < 1
SOLUTION:3t + 2 < -7 -4t + 5 < 1
3t < -7 -2 -4t < 1 - 5
t < -3 -4t < -4
3t < -9
t > 1
or
Interval: (-∞,-3) U (1, ∞)
Real-World:You have taken a quiz and got
55%. 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 between 70% and 79% What are the possible
percentages you must get on the next quiz?
Real-World: (SOLUTION)Quiz 1 = 55%
Quiz 2 = x%
Average
70% and 79%
70%
Thus in order for you to obtain a passing grade in your quizzes, you must get between 85% and 103% on your next quiz? (Good Luck!!!)
140
85
Real-World:A secondary 15-year old student should
consume no more than 2200 calories per day. A moderately active student should
consume between 2400 and 2800. An active 15-year-old student should consume between 2800 and 3200
calories per day. Model these ranges on a number line and represent them
in set and interval notations.
SOLUTION:A secondary 15-year old student
should consume no more than 2200 calories per day.
0 1000 2000
Set: { x | 0 < x ≤ 2200} Interval: (0, 2200]
2200
SOLUTION:A moderately active student should consume between 2400 and 2800
Calories per day.
0 1000 2000
Set: { x | 2400 < x ≤ 2800} Interval: (2400, 2800)
2800
3000
2400
SOLUTION:An active 15-year-old student should
consume between 2800 and 3200 calories per day.
0 1000 2000
Set: { x | 2800 < x ≤ 3200} Interval: (2800, 3200)
3200
3000
2800
VIDEOS: Compoundinequalities
https://www.khanacademy.org/math/algebra/linear_inequalities/compound_absolute_value_inequali/v/compund-inequalities
https://www.khanacademy.org/math/algebra/linear_inequalities/compound_absolute_value_inequali/v/compound-inequalities
VIDEOS: Compoundinequalities
https://www.khanacademy.org/math/algebra/linear_inequalities/compound_absolute_value_inequali/v/compound-inequalities-3
https://www.khanacademy.org/math/algebra/linear_inequalities/compound_absolute_value_inequali/v/compund-inequalities-2
CLASSWORK:
Page 204-206
Problems: As many as needed to master the
concept.