Download Solving Compound Inequalities - Miami Beach Senior High School

Name:
Date:
Period:
Topic: Solving & Graphing Compound Inequalities
Essential 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.
2.
3.
4.
5.
6.
5>x
5<x
x > 10
5≥x
5≤x
x < 10
a)
- 10
-5
0
5
10
- 10
-5
0
5
10
- 10
-5
0
5
10
- 10
-5
0
5
10
- 10
-5
0
5
10
b)
c)
d)
e)
Home-Learning Assignment #1 – Review:
Do you remember the difference
between and and or on Set Theory?
A
B
A
B
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
Vocabulary:
Compound Inequality
A compound inequality consist
of two inequalities connected by
and or or.
Guided Example:
Graph x < 4 and x ≥ 2
a) Graph x < 4
o
2
3
4
3
4
b) Graph x ≥ 2
●
2
c) What if I Combine the graphs?
d) Where do they intersect?
●
2
3
o
4
Guided Example:
Graph x < 2 or x ≥ 4
a) Graph x < 2
o
2
b) Graph x ≥ 4
2
3
3
c) Combine the graphs
4
●
4
1) Which inequalities describe the
following graph?
o
o
1.
2.
3.
4.
-3
-2
y > -3 or y < -1
y > -3 and y < -1
y ≤ -3 or y ≥ -1
y ≥ -3 and y ≤ -1
-1
Lets graph the compound inequality
6<m<8
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.
o
6
7
o
8
2) Which is equivalent to
-3 < y < 5?
1.
2.
3.
4.
y > -3 or y < 5
y > -3 and y < 5
y < -3 or y > 5
y < -3 and y > 5
1.
2.
3.
4.
3) Which is equivalent to
x > -5 and x ≤ 1?
-5 < x ≤ 1
-5 > x ≥ 1
-5 > x ≤ 1
-5 < x ≥ 1
All real numbers that are greater
than – 2 and less than 6
-2<x<6
All real numbers that are less
than 0 or greater than or equal to 5
x < 0 or x ≥ 5
Guided Example:
All real numbers that are greater than zero and less than or equal to 4.
0 x4
All real numbers that are less than –1 or greater than 2
x  1or x  2
4) Graph x < 2 or x ≥ 4
5) Graph x ≥ -1 or x ≤ 3
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
8) x is less than 4 and is at least -9
a.)4  x  9
b.)  9  x  4
c.)  9  x  4
d .)  9  x  4
Solving & Graphing
and
and
3 < 2m – 1 < 9
and
HINT: ONLY “AND” PROBLEMS WILL LOOK LIKE
THIS. “OR” PROBLEMS MUST SAY “OR”
and
Answer:
3 < 2m – 1 < 9
+1
+1 +1
-----------------------------4 < 2m
< 10
2
2
2
2 < m <5
-5
0
5
3 x  8  17 or 2 x  5  7
Answer:
3 x  8  17 or 2 x  5  7
–8
–8
3x > 9
3
3
x>3
–5 –5
2x ≤ 2
2
2
x≤1
9)
 2  3x  8  10
10)
3x  1  4 or 2 x  5  7
11)
- 3 < - 1 – 2x ≤ 5
12)
6  x 6 8
13)
14)
13  5  2x  9
-15 ≤ –3x – 21 ≤ 25
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)
Based on the meaning of ‘and,’ why is this No Solution ?
2x < -6 and 3x ≥ 12
1. Solve each inequality
for x
2. Graph each inequality
3. Combine the graphs
4. Where do they
intersect?
5. They do not! x cannot
be greater than or equal
to 4 and less than -3
No Solution!!
2 x 6

2
2
x  3
o
-3
3x 12

3
3
x4
0
4
7
-6
1
o
●
Wrap-Up:
Vocabulary Review
Summary
Home-Learning Assignment #2:
Page 204 – 206 (9, 16, 18, 37, 54)