CHAPTER 5SYSTEMS

CREATED AT WORDLE.NET

SECTION 5-1INEQUALITIES AND COMPOUND SENTENCES

WARM-UP

Refer to the postal regulations listed on page 271.1. Find the volume of the smallest postcard that can be

mailed for $.20.

2. Find the volume of the largest postcard that can be mailed for $.20.

3. Use the answers from the two questions above. Find the approximate ratio of the largest volume to the smallest

volume.

WARM-UP

Refer to the postal regulations listed on page 271.1. Find the volume of the smallest postcard that can be

mailed for $.20..007” X 3.5” X 5”

2. Find the volume of the largest postcard that can be mailed for $.20.

3. Use the answers from the two questions above. Find the approximate ratio of the largest volume to the smallest

volume.

WARM-UP

Refer to the postal regulations listed on page 271.1. Find the volume of the smallest postcard that can be

mailed for $.20..007” X 3.5” X 5” = .1225 cubic inches

2. Find the volume of the largest postcard that can be mailed for $.20.

3. Use the answers from the two questions above. Find the approximate ratio of the largest volume to the smallest

volume.

WARM-UP

Refer to the postal regulations listed on page 271.1. Find the volume of the smallest postcard that can be

mailed for $.20..007” X 3.5” X 5” = .1225 cubic inches

.25” X 4.25” X 6”

2. Find the volume of the largest postcard that can be mailed for $.20.

3. Use the answers from the two questions above. Find the approximate ratio of the largest volume to the smallest

volume.

WARM-UP

Refer to the postal regulations listed on page 271.1. Find the volume of the smallest postcard that can be

mailed for $.20..007” X 3.5” X 5” = .1225 cubic inches

.25” X 4.25” X 6” = 6.375 cubic inches

2. Find the volume of the largest postcard that can be mailed for $.20.

3. Use the answers from the two questions above. Find the approximate ratio of the largest volume to the smallest

volume.

WARM-UP

Refer to the postal regulations listed on page 271.1. Find the volume of the smallest postcard that can be

mailed for $.20..007” X 3.5” X 5” = .1225 cubic inches

.25” X 4.25” X 6” = 6.375 cubic inches

2. Find the volume of the largest postcard that can be mailed for $.20.

3. Use the answers from the two questions above. Find the approximate ratio of the largest volume to the smallest

volume.

6.375

.1225

WARM-UP

Refer to the postal regulations listed on page 271.1. Find the volume of the smallest postcard that can be

mailed for $.20..007” X 3.5” X 5” = .1225 cubic inches

.25” X 4.25” X 6” = 6.375 cubic inches

2. Find the volume of the largest postcard that can be mailed for $.20.

3. Use the answers from the two questions above. Find the approximate ratio of the largest volume to the smallest

volume.

6.375

.1225 ≈ 52

1

INEQUALITY:

INEQUALITY: A sentence that contains one of the following symbols: ≤,≥,<,>,≠

INEQUALITY: A sentence that contains one of the following symbols: ≤,≥,<,>,≠

COMPOUND SENTENCE:

INEQUALITY: A sentence that contains one of the following symbols: ≤,≥,<,>,≠

COMPOUND SENTENCE: A sentence where two clauses are connected by “and” or “or”

EXAMPLE 1

As of 1994, recorded temperatures in the state of Michigan have ranged from a low of -51℉ in Vanderbilt (1934) to

112℉ in Mio (1936). Graph the range of recorded temperatures.

EXAMPLE 1

As of 1994, recorded temperatures in the state of Michigan have ranged from a low of -51℉ in Vanderbilt (1934) to

112℉ in Mio (1936). Graph the range of recorded temperatures.

-60 -30 0 30 60 90 120

EXAMPLE 1

As of 1994, recorded temperatures in the state of Michigan have ranged from a low of -51℉ in Vanderbilt (1934) to

112℉ in Mio (1936). Graph the range of recorded temperatures.

-60 -30 0 30 60 90 120

INTERSECTION:

INTERSECTION: The common elements of more than one set; The elements must be in both sets. (and)

INTERSECTION: The common elements of more than one set; The elements must be in both sets. (and)

Notation :

INTERSECTION: The common elements of more than one set; The elements must be in both sets. (and)

Notation :

UNION:

INTERSECTION: The common elements of more than one set; The elements must be in both sets. (and)

Notation :

UNION: The set consists of elements in either one or both sets. (or)

INTERSECTION: The common elements of more than one set; The elements must be in both sets. (and)

Notation :

UNION: The set consists of elements in either one or both sets. (or)

Notation :

EXAMPLE 2

People from age 16 to 65 can give blood at a blood bank.

a. Write a compound inequality to describe the possible ages A at which blood can be given.

EXAMPLE 2

People from age 16 to 65 can give blood at a blood bank.

a. Write a compound inequality to describe the possible ages A at which blood can be given.

16 ≤ A ≤ 65

EXAMPLE 2

People from age 16 to 65 can give blood at a blood bank.

a. Write a compound inequality to describe the possible ages A at which blood can be given.

16 ≤ A ≤ 65

b. Graph the inequality on a number line.

EXAMPLE 2

People from age 16 to 65 can give blood at a blood bank.

a. Write a compound inequality to describe the possible ages A at which blood can be given.

16 ≤ A ≤ 65

b. Graph the inequality on a number line.

0 40 60 8020

EXAMPLE 2

People from age 16 to 65 can give blood at a blood bank.

a. Write a compound inequality to describe the possible ages A at which blood can be given.

16 ≤ A ≤ 65

b. Graph the inequality on a number line.

0 40 60 8020

PROPERTIES OF INEQUALITY

ADDITION PROPERTY OF INEQUALITY

MULTIPLICATION PROPERTIES OF INEQUALITY

PROPERTIES OF INEQUALITY

For all real numbers a, b, and c:

ADDITION PROPERTY OF INEQUALITY

MULTIPLICATION PROPERTIES OF INEQUALITY

PROPERTIES OF INEQUALITY

For all real numbers a, b, and c:

ADDITION PROPERTY OF INEQUALITY

If a < b, then a + c < b + c

MULTIPLICATION PROPERTIES OF INEQUALITY

PROPERTIES OF INEQUALITY

For all real numbers a, b, and c:

ADDITION PROPERTY OF INEQUALITY

If a < b, then a + c < b + c

MULTIPLICATION PROPERTIES OF INEQUALITY

If a < b and c > 0, then ac < bc

PROPERTIES OF INEQUALITY

For all real numbers a, b, and c:

ADDITION PROPERTY OF INEQUALITY

If a < b, then a + c < b + c

MULTIPLICATION PROPERTIES OF INEQUALITY

If a < b and c > 0, then ac < bc

If a < b and c < 0, then ac > bc

EXAMPLE 3

Solve 3x - 4 ≤ 26 and graph the solution set.

EXAMPLE 3

Solve 3x - 4 ≤ 26 and graph the solution set.

3x - 4 ≤ 26

EXAMPLE 3

Solve 3x - 4 ≤ 26 and graph the solution set.

3x - 4 ≤ 26+4 +4

EXAMPLE 3

Solve 3x - 4 ≤ 26 and graph the solution set.

3x - 4 ≤ 26+4 +4

3x ≤ 30

EXAMPLE 3

Solve 3x - 4 ≤ 26 and graph the solution set.

3x - 4 ≤ 26+4 +4

3x ≤ 303 3

EXAMPLE 3

Solve 3x - 4 ≤ 26 and graph the solution set.

3x - 4 ≤ 26+4 +4

3x ≤ 303 3x ≤ 10

EXAMPLE 3

Solve 3x - 4 ≤ 26 and graph the solution set.

3x - 4 ≤ 26+4 +4

3x ≤ 303 3x ≤ 10

-4 4 8 120

EXAMPLE 3

Solve 3x - 4 ≤ 26 and graph the solution set.

3x - 4 ≤ 26+4 +4

3x ≤ 303 3x ≤ 10

-4 4 8 120

REMEMBER!!!

WHEN MULTIPLYING OR DIVIDING BY A NEGATIVE, REMEMBER TO FLIP THE INEQUALITY SIGN!

EXAMPLE 4

An airplane flying at 34,000 feet descends at the rate of 2500 feet per minute. After how many minutes will the

plane be below 20,000 feet?

EXAMPLE 4

An airplane flying at 34,000 feet descends at the rate of 2500 feet per minute. After how many minutes will the

plane be below 20,000 feet?

m = minutes

EXAMPLE 4

An airplane flying at 34,000 feet descends at the rate of 2500 feet per minute. After how many minutes will the

plane be below 20,000 feet?

m = minutes34,000 - 2500m < 20,000

EXAMPLE 4

An airplane flying at 34,000 feet descends at the rate of 2500 feet per minute. After how many minutes will the

plane be below 20,000 feet?

m = minutes34,000 - 2500m < 20,000

-34,000 -34,000

EXAMPLE 4

An airplane flying at 34,000 feet descends at the rate of 2500 feet per minute. After how many minutes will the

plane be below 20,000 feet?

m = minutes34,000 - 2500m < 20,000

-34,000 -34,000- 2500m < -14,000

EXAMPLE 4

An airplane flying at 34,000 feet descends at the rate of 2500 feet per minute. After how many minutes will the

plane be below 20,000 feet?

m = minutes34,000 - 2500m < 20,000

-34,000 -34,000- 2500m < -14,000

-2500 -2500

EXAMPLE 4

An airplane flying at 34,000 feet descends at the rate of 2500 feet per minute. After how many minutes will the

plane be below 20,000 feet?

m = minutes34,000 - 2500m < 20,000

-34,000 -34,000- 2500m < -14,000

-2500 -2500m > 5.6

EXAMPLE 4

An airplane flying at 34,000 feet descends at the rate of 2500 feet per minute. After how many minutes will the

plane be below 20,000 feet?

m = minutes34,000 - 2500m < 20,000

-34,000 -34,000- 2500m < -14,000

-2500 -2500m > 5.6

After 5 minutes and 36 seconds, the plane will be below 20,000 feet

EXAMPLE 5

Graph

x : x < 3 x ≥ π{ }.

EXAMPLE 5

Graph

x : x < 3 x ≥ π{ }.

2.8 3 3.1 3.22.9

EXAMPLE 5

Graph

x : x < 3 x ≥ π{ }.

2.8 3 3.1 3.22.9

EXAMPLE 5

Graph

x : x < 3 x ≥ π{ }.

2.8 3 3.1 3.22.9

HOMEWORK

HOMEWORK

p. 276 #1-25, skip 22

“To accomplish our destiny it is not enough to merely guard prudently against road accidents. We must also cover before nightfall the distance assigned to each of us.” - Alexis Carrel