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Name:Date:Period: Topic: Solving & Graphing Compound InequalitiesEssential Question: How does a compound inequality differ from a regular inequality? What is the meaning of “and” and “or” in a compound inequality? Warm-Up:Match the following graphs with its’ corresponding inequality:
1.5 > x a)
2.5 < x
3.x > 10
4.5 ≥ x
5.5 ≤ x
6.x < 10
0
0
0
0
0
5
5
5
- 5
- 5
- 5
- 5
- 5
5
5
10
10
10
10
10
- 10
- 10
- 10
- 10
- 10
b)
d)
e)
c)
Home-Learning Assignment #1 – Review:
Do you remember the difference between and and or on Set Theory?
AND means intersection-what do the two items
have in common?
OR means union-if it is in one item, it is in
the solution
A
A B
B
Compound Inequality
A compound inequality consist of two inequalities connected by
and or or.
Vocabulary:
Graphing Compound
Graphing Compound
Inequalities
Inequalities
Graph x < 4 and x ≥ 2
3 42●
a) Graph x < 4
b) Graph x ≥ 23 42
o
c) What if I Combine the graphs?
●
3 42o
d) Where do they intersect?●
3 42o
Guided Example:
Graph x < 2 or x ≥ 4
3 42●
a) Graph x < 2
b) Graph x ≥ 43 42
o
c) Combine the graphs
3 42o
3 42●
Guided Example:
1) Which inequalities describe the following graph?
-2 -1-3oo
1. y > -3 or y < -1
2. y > -3 and y < -1
3. y ≤ -3 or y ≥ -1
4. y ≥ -3 and y ≤ -1
When written this way, it is the same thing as
6 < m AND m < 8
It can be rewritten as m > 6 and m < 8 and graphed as previously shown.
Lets graph the compound inequality 6 < m < 8
7 86oo
2) Which is equivalent to-3 < y < 5?
1. y > -3 or y < 5
2. y > -3 and y < 5
3. y < -3 or y > 5
4. y < -3 and y > 5
3) Which is equivalent to x > -5 and x ≤ 1?
1. -5 < x ≤ 1
2. -5 > x ≥ 1
3. -5 > x ≤ 1
4. -5 < x ≥ 1
Writing Compound
Writing Compound
Inequalities
Inequalities
All real numbers that are greater than – 2 and less than 6
All real numbers that are less than 0 or greater than or equal to 5
- 2 < x < 6
x < 0 or x ≥ 5
All real numbers that are greater than zero and less than or equal to 4.
40 x
All real numbers that are less than –1 or greater than 2
21 xorx
Guided Example:
6) All real numbers that are greater than or equal to – 4 and less than 6
7) All real numbers that are less than or equal to 2.5 or greater than 6
4) Graph x < 2 or x ≥ 4
5) Graph x ≥ -1 or x ≤ 3
8) x is less than 4 and is at least -9
49.)
49.)
49.)
94.)
xd
xc
xb
xa
Solving & Graphing
Compound Inequaliti
es
3 < 2m – 1 < 9
andand
andand
andand
andandHINT: ONLY “AND” PROBLEMS WILL LOOK LIKE
THIS. “OR” PROBLEMS MUST SAY “OR”
Solving & Graphing
3 < 2m – 1 < 9
0 5-5
Answer:
+ 1 + 1 + 1------------------------------ 4 < 2m < 10 2 2 2
2 < m < 5
7521783 xorx
Answer:7521783 xorx
– 8 – 8 3x > 9 3 3 x > 3
– 5 – 5 2x ≤ 2 2 2 x ≤ 1
866 x
92513 x
- 3 < - 1 – 2x ≤ 511)
12)
13)
-15 ≤ –3x – 21 ≤ 2514)
10832 x752413 xorx10)
9)
Additional Practice:
Page 204 - 206 (1 – 8, 14, 36)
For those who complete the work before time is over, proceed to work on the following problems:Page 204 - 206 (10, 15, 24, 26, 38, 41, 55)
2x < -6 and 3x ≥ 12
1. Solve each inequality for x
2. Graph each inequality3. Combine the graphs4. Where do they
intersect?5. They do not! x cannot
be greater than or equal to 4 and less than -3 No Solution!!
2 6
2 2 3
x
x
3x 12
3 3 x 4
-3 0-6o-3 0-6o
4 71o●4 71o●
Based on the meaning of ‘and,’ why is this No Solution ?
Wrap-Up:Vocabulary Review
Summary
Home-Learning Assignment #2:Page 204 – 206 (9, 16, 18, 37, 54)