Compound Inequalities (A1 1-6)
Presentation
•
Mathematics
•
7th - 10th Grade
•
Medium
Erica Nafziger
Used 19+ times
FREE Resource
11 Slides • 10 Questions
1
Compound Inequalities (A1 1-6)
ESSENTIAL
QUESTION
WHAT ARE COMPOUND INEQUALITIES AND HOW ARE THEIR SOLUTIONS REPRESENTED?
2
COMPOUND INEQUALITY
Two inequalities (or more) joined together with "and" or "or".
3
TYPE 1: "OR" :
"or" inequalities tend to graph apart
<----- or ----->
4
example 1:
FIrst, solve the inequalities for the given variable.
5
example 1:
Once you solve the inequalities, it is time to graph!
Graph just as you would any other Inequality. Notice how the two inequalities go in opposite directions.
6
example 2:
7
Multiple Choice
Solve the following Compound Inequality: 2x+9≥17 or 5x+10<10
x>4 or x≥0
x≥4 or x>0
x≤4 or x≥0
x≥4 or x<0
8
Multiple Choice
Does the following graph match the compound inequality: x≥4 or x<0
TRUE
FALSE
9
Multiple Choice
Solve the following Compound Inequality: 7x−14≥0 or 4x+5≤−3
x≤−2 or x>2
x≤−2 or x≥2
x≤2 or x>−2
x<−2 or x>2
10
Multiple Choice
Solve the following Compound Inequality: −3(2x+1)<−15 or 1−x≥5
x≥2 or x≤−4
x≥−4 or x<2
x≤−4 or x>2
x<−4 or x>2
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TYPE 2: "AND" :
"and" inequalities have a tendency to graph together
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TYPE 2: "AND" :
Because "and" solutions fall between two endpoints, they can be written in a condensed form:
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Solving "and":
MUST split the compound inequality into two inequalities.
You can use the box method to help you split the compound inequality in two. Notice in the picture how everything in the middle is included when splitting it in two.
14
Solving "and":
Once you solve the inequalities, it is time to graph! Graph just as you would any other Inequality. Notice how the two inequalities go towards each other.
15
ex. 2:
16
Multiple Choice
Solve the following "and" Compound Inequality: −27<7x−13<8
x>−2 and x<3
x>−2 and x>3
x<−2 and x<3
x>2 and x<3
17
Multiple Choice
Which compound inequality matches the following "And" Compound Inequality: x>−2 and x<3
−2<x<3
−2>x<3
18
Multiple Choice
Which graph matches the following "And" Compound Inequality: x>−2 and x<3
19
Multiple Choice
Solve the following Compound Inequality: −3<2x+3≤15
x>−3 and x≥6
x<−3 and x<6
−3>x≤6
x>−3 and x≤6
20
Multiple Select
Solve the following the Compound Inequality: −2<2(x−6)≤4
5<x≤8
x<5 and x≥8
5>x≥8
x>5 and x≤8
21
Poll
How do you feel about solving Compound Inequalities?
Great!
Good
Okay
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Compound Inequalities (A1 1-6)
ESSENTIAL
QUESTION
WHAT ARE COMPOUND INEQUALITIES AND HOW ARE THEIR SOLUTIONS REPRESENTED?
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