Inequalities

1
Inequalities

• Graphing and Solving Basic Inequalities

2
Inequalities

• Must have at least 12 credits to be considered a
  full-time student.
• In a typical 2000 calorie diet, it is recommended
  that you consumeno more than 65 grams of fat.

3
Inequalities

• A voltmeter is designed so that any reading is in
  error by no more than 1.2 V.
• If a measurement reading indicates 10.8 V, use an
  inequality to describe the possible values for
  the voltage.

1.2 V
1.2 V
Reading
lt
lt
R
12.0 V
9.6 V
4
Inequalities

• Notation allows us to describe how one quantity
  compares to another.

A lt B
A gt B
A B
A B
5
Inequalities

• Sense refers to the direction of inequality
  sign.
• a lt b and c lt d have the same sense.
• a lt b and c gt d have opposite senses.

6
Writing Inequalities
x
lt
-5
7
Graphing Inequalities

• Inequality relationships can be depicted using a
  number line.

8
Graphing Inequalities

• x gt 4

1
2
3
4
5
6
7
8
9
9
Graphing Inequalities

• x 11

5
6
7
8
9
10
11
12
13
10
Graphing Inequalities

• Represent the following relationship using
  inequality notation.

5
6
7
8
9
10
11
12
13
W
11
Graphing Inequalities

• Represent the following relationship using
  inequality notation.

-15
-14
-13
-12
-11
-10
-9
-8
-7
W
12
Solving Inequalities
13
Solving Inequalities

• Just like equation, inequalities arise when
  representing a situation.
• Karens financial aid stipulates that her tuition
  not exceed 1000. If her college charges 35 for
  registration and 375 per course, what is the
  greatest number of courses she can take?

Registration and Tuition cant go beyond 1000
35 375 x number of credits lt 1000
14
Solving Inequalities

• Inequality
• 35375c lt 1000

• Equation
• 35375c 1000

-35 -35
-35 -35
375c 965
375c lt 965
c lt 2.57333
c 2.57333
15
Solving Inequalities

• Solve the following inequality and graph the
  solution on a number line
• 3x 4 gt 2x 1

-2x -2x
4 4
x gt 5
16
Solving Inequalities (Dealing w/ Multiplication
and Division)

• What happens if the same number is multiplied to
  each side of
• 2 lt 5
• 2(4) lt 5(4)
• 8 lt 20

17
Solving Inequalities (Dealing w/ Multiplication
and Division)

• What happens if the same number is multiplied to
  each side of
• 2 lt 5
• 2(-3) lt 5(-3)
• -6 lt -15
• -6 gt -15

18
Solving Inequalities (Dealing w/ Multiplication
and Division)

• What happens if each quantity is divided by the
  same number
• 12 lt 15
• 12/3 lt 15/3
• 4 lt 5

19
Solving Inequalities (Dealing w/ Multiplication
and Division)

• What happens if each quantity is divided by the
  same number
• 12 lt 15
• 12/-3 lt 15/-3
• -4 lt -5
• -4 gt -5

20
Solving Inequalities

• Solve the following inequality and graph the
  solution on a number line

(3)
(3)
x lt 15
21
Solving Inequalities

• Solve the following inequality and graph the
  solution on a number line
• -4x 28

-4 -4
x -7
gt
lt
22
Solving Inequalities

• Solve the following inequality and graph the
  solution on a number line
• 3x 4 lt 5x - 8

-3x -3x
8 8
12 lt 2x
2 2
6 lt x
x gt 6
23
Solving Inequalities

• Solve the following inequality and graph the
  solution on a number line

6y 9 gt 21
6y gt 30
y gt 5
24
Practice

• MathXL Ch 4 Section 3 Homework