1. October 28, 2013
Today:
Khan Due Tomorrow
Finals Next Week
Warm Up
Compound Inequalities
Class Work

2. Warm Up
1)Three –fourths of the difference between a number
and six is no more than the quotient of that number
and four
4. Glynn has to drive 450 miles. His car has an 18
gallon gas tank and he would like to make the trip on
one tank of gas. What is the minimum miles per
gallon his car would have to get to make the trip on
one tank? Write an inequality to show .

3. Warm Up
5. Solve for x if ax + by = c
6. -3(2x - 3) + 7x = -4(x - 5) + 6x – 2
7. Simplify: -6 - (-3) + (-2) * 4 =
8.
|
|
10. -2 x - 7 - 4 = -22

4. Solving Compound
Inequalities

5. Solving Compound Inequalities
A compound inequality consists of two inequalities joined
by the word and or the word or.
A. Conjunctions: Two inequalities joined by the word ‘and’.
For example: -1 < x and x < 4; This can also be written -1 < x < 4
To solve a compound inequality, you must solve each part
of the inequality separately. Conjunctions are solved when
both parts of the inequality are true -1 < x < 4; x > -1 < 4
x
-1
4
The graph of a compound inequality containing the word ‘and’
is the intersection of the solution set of the two inequalities. The
Intersection is the solution for the compound inequality.

6. Solving Compound Inequalities
All compound inequalities divide the number line into
three separate regions.
x
y
z
A compound inequality containing the word and is true
if and only if (iff), both inequalities are true.

7. Solving Compound Inequalities
A compound inequality containing the word and is true
if and only if (iff), both inequalities are true.
Example:
x
1
x
-5
-4
-3
-2
-1
0
1
2
3
4
5

8. Solving Compound Inequalities
A compound inequality containing the word and is true if
and only if (iff), both inequalities are true.
Example:
x
x
1
2
x
-5
-4
-3
-2
-1
0
1
2
3
4
5
x
-5
-4
-3
-2
-1
0
1
2
3
4
5

9. Solving Compound Inequalities
A compound inequality containing the word and is true if
and only if (iff), both inequalities are true.
Example:
x
x
1
2
x
-4
-3
-2
-1
0
1
2
3
4
5
x
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
0
1
2
3
4
5
1
and
x
x
-5
2
x

10. Solving Compound Inequalities
x
-5
-4
-3
-2
-1
0
1
2
3
4
5
This conjunction can also be written without the word ‘and’.
-1 < x < 2

11. Solving Compound Inequalities
Practice Problem: Compound Inequality
(Conjunction)
1. -2 < x – 1< 3 How would we write this
using the word ‘and’?
1.
x > -2 and x – 1< 3
The Solution is: -1 < x < 4
x
-5
-5
-4
-3
-2
-1
0
1
2
3
4
5
5

12. Solving Compound Inequalities
Practice Problem: Compound Inequality
(Conjunction)
2.
x < -2 and x – 2 > 1
The Solution is:
No Solution

13. Solving Compound Inequalities
B. Disjunction: A compound inequality containing the word
‘or’, is true if one or both inequalities are true.
x
Example:
x 1
-5
-4
-3
-2
-1
0
1
2
3
4
5

14. Solving Compound Inequalities
B. Disjunction: A compound inequality containing the word
‘or’, is true if one or both inequalities are true.
Example:
x 1
x 3
x
-5
-4
-3
-2
-1
0
1
2
3
4
5
x
-5
-4
-3
-2
-1
0
1
2
3
4
5

15. Solving Compound Inequalities
B. Disjunction: A compound inequality containing the word
‘or’, is true if one or both inequalities are true.
Example:
x 1
x 3
x
-5
-4
-3
-2
-1
0
1
2
3
4
5
x
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
0
1
2
3
4
5
x 1
or
x 3
x

16. Solving Compound Inequalities
B. Disjunction: A compound inequality containing the word
‘or’, is true if one or both inequalities are true.
Example:
x 1
or
x 3
x
-5
-4
-3
-2
-1
0
1
2
3
4
5

17. Solving Compound Inequalities
Practice Problem: Compound Inequality
(Disjunction)
1. 2x + 1 < 5 or 3x > x + 8
The Solution is:
x < 2 or x > 4
x
-5
-5
-4
-3
-2
-1
0
1
2
3
4
5
5