Chapter 2.6(a) Solving Compound Inequalities.notebook
September 16, 2016
Bellwork:
Chapter 2.6(a) Solving Compound Inequalities
Multiply/Divide
1)
2)
3)
Solve compound inequalities in one variable and graph the solution sets.
Solve and graph the following inequality:
4) ­3(2r ­ 4) ≥ 2(5 ­ 3r)
Sep 15­9:21 AM
Sep 15­9:27 AM
Solve and graph the following inequalities. What is important to remember when solving?
Compound Inequality: when two simple inequalities are joined by the words and or or.
Words
1) 2) All real numbers greater than 2 AND less than 6
Algebra
x > 2 and x < 6
Graph
2 < x < 6
All real numbers greater x ≥ 2 and x ≤ 6
than or equal to 2 AND less than or equal to 6
2 ≤ x ≤6
All real numbers less than x < 2 or x > 6
2 OR greater than 6
All real numbers less than or equal to 2 OR greater x ≤ 2 or x ≥ 6
than or equal to 6
Sep 3­10:20 AM
Sep 15­9:36 AM
The pH level of a popular shampoo is between 6.0 and 6.5 inclusive. Write a compound inequality to show the pH levels of this shampoo. Graph the solutions.
Writing a Compound Inequality from a Graph:
6)
­5
­4
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­2
­1
0
1
2
3
4
5
­5
­4
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­2
­1
0
1
2
3
4
5
7)
The overlapping section of the number line is called the intersection. The intersection shows the solutions that are true for both inequalities.
8)
­5
­4
­3
­2
­1
0
1
2
3
4
5
­5
­4
­3
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0
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3
4
5
Graph the intersection of the following inequalities:
9) 5 < y ≤ 9
Sep 15­9:54 AM
Sep 15­9:41 AM
1
Chapter 2.6(a) Solving Compound Inequalities.notebook
Solve each compound inequality and graph the solution.
September 16, 2016
Graphing a compound inequality containing the word or.
x < ­8 or x > 2
1) 2x < 0 and 4x > ­12
The combined regions are called the union. The union shows the solutions that are true for either inequalities.
2) 8 < 3x ­ 1 ≤ 11
3) ­5 < x + 1 < 2
Sep 15­9:44 AM
Sep 15­9:49 AM
Solving compound Inequalities Involving OR:
Solve and graph the solutions for the following inequalities
What is the difference between a compound inequality containing the word and and one containing the word or?
4) 8 + t ≥ 7 or 8 + t < 2
5) 4x ≤ 20 or 3x > 21
Sep 15­9:52 AM
Sep 15­10:00 AM
Homework:
P. 138­140 #1­41 (odds)
Sep 15­10:01 AM
2