Chapter 6 Sec 3

1
Chapter 6 Sec 3

• Solving Multi-Step Inequalities
• Involving one operation
• Involving Distributive Property

2
Real World
The boiling point of a substance is the
temperature at which the element changes from a
liquid to a gas. The boiling point of chlorine
is 31o F. If F represents temp in Fahrenheit,
the inequality F gt 31 represents the temps where
chlorine is a gas. If C is Celsius, the F 9/5 C
32so
9 5
C 32 gt 31
32 32
Solve for C
9 5
C gt (63)
C gt 35
C C gt -35
3
Negative Coefficient
Solve 7b 19 lt 16.
7b 19 lt 16 7b lt 35 b gt 5
19 19
7 7
b b gt 5
4
Write and solve an inequality
Write an inequality for the sentence below. Then
solve the inequality.
Three times a number minus eighteen is at least
five times that number plus twenty-one.
five times that number
is at least
Three times a number
plus
twenty-one
minus
eighteen
3n 18 gt
5n 21
5n 5n
3n 18 gt 5n 21 2n 18 gt 21
2n gt 39 n lt 19.5
18 18
n n lt 19.5
2 2
5
Distributive Property
Solve 3d 2(8d 9) gt 3 (2d 7).
3d 2(8d 9) gt 3 (2d 7) 3d 16d 18 gt 3
2d 7 13d 18 gt 2d 4 18 gt
11d 4 22 gt 11d 2 gt d
13d 13d
4 4
11 11
d d lt 2
6
Empty Set
Solve 8(t 2) 3(t 4) lt 5(t 7) 8.
8(t 2) 3(t 4) lt 5(t 7) 8 8t 16 3t
12 lt 5t 35 8 5t 28 lt 5t 27 28 lt
27
- 5t - 5t
This is a false statement.
Since the inequality results in a false
statement, the solution set is the empty set.
7
Chapter 6 Sec 4

• Solving Compound Inequalities
• Involving the word and
• Involving the word or

8
Inequalities Containing and

• A compound inequality is true only if both
  inequalities are true. Thus the graph of a
  compound inequality containing and is the
  intersection of the graphs.
• In other words the solution must be both
  inequalities

9
Graph an Intersection

• Graph the solution set of x lt 3 and x gt 2

x lt 3
x gt 2
10
Solve and Graph an Intersection
Solve 5 lt x 4 lt 2.
5 lt x 4 1 lt x x gt 1
x 4 lt 2 x lt 6
4 4
4 4
11
Inequalities Containing or

• A compound inequality containing or is true if
  one or more of the inequalities is true. Thus
  the graph of a compound inequality containing or
  is the union of the graphs.
• In other words the solution is a solution of
  either inequality

12
Graph an Union

• Graph the solution set of x lt 1 or x gt 2

x lt 1
x gt 2
13
Solve and Graph a Union
Solve 3h 4 lt 19 or 7h 3 gt 18.
4 4
7h 3 gt 18 7h gt 21 h gt 3
3 3
3h 4 lt 19 3h lt 15 h gt 5
or
7 7
3 3
14
Homework Ch 6 Sec 3 4

• Study Guide (SG)
• Pgs 85 88 Even
• FCA 5 Worksheet due Dec 10th
• Vocabulary Quiz Fri, Dec 12th
• Semester Exam Tuesday, Dec 16th