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( 11 a + 3 ) 18 a = −4

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4 z 2 z ( 1 + 4 ) = 36

−6

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4 y ( 7 2 ) 2 = −200

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( 2 x ) 2 + 1 = −3

± 1

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8 ( 2 + 4 ) 15 b = b

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1 4 ( 8 w 4 2 ) = 0

2

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For the following exercises, simplify the expression.

2 y ( 4 ) 2 y 11

−14 y 11

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a 2 3 ( 64 ) 12 a ÷ 6

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8 b 4 b ( 3 ) + 1

−4 b + 1

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5 l ÷ 3 l × ( 9 6 )

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7 z 3 + z × 6 2

43 z 3

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4 × 3 + 18 x ÷ 9 12

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9 ( y + 8 ) 27

9 y + 45

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6 + 12 b 3 × 6 b

−6 b + 6

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( 4 9 ) 2 × 27 x

16 x 3

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8 ( 3 m ) + 1 ( 8 )

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9 x + 4 x ( 2 + 3 ) 4 ( 2 x + 3 x )

9 x

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Real-world applications

For the following exercises, consider this scenario: Fred earns $40 mowing lawns. He spends $10 on mp3s, puts half of what is left in a savings account, and gets another $5 for washing his neighbor’s car.

Write the expression that represents the number of dollars Fred keeps (and does not put in his savings account). Remember the order of operations.

1 2 ( 40 10 ) + 5

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How much money does Fred keep?

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For the following exercises, solve the given problem.

According to the U.S. Mint, the diameter of a quarter is 0.955 inches. The circumference of the quarter would be the diameter multiplied by π . Is the circumference of a quarter a whole number, a rational number, or an irrational number?

irrational number

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Jessica and her roommate, Adriana, have decided to share a change jar for joint expenses. Jessica put her loose change in the jar first, and then Adriana put her change in the jar. We know that it does not matter in which order the change was added to the jar. What property of addition describes this fact?

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For the following exercises, consider this scenario: There is a mound of g pounds of gravel in a quarry. Throughout the day, 400 pounds of gravel is added to the mound. Two orders of 600 pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,200 pounds of gravel.

Write the equation that describes the situation.

g + 400 2 ( 600 ) = 1200

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For the following exercise, solve the given problem.

Ramon runs the marketing department at his company. His department gets a budget every year, and every year, he must spend the entire budget without going over. If he spends less than the budget, then his department gets a smaller budget the following year. At the beginning of this year, Ramon got $2.5 million for the annual marketing budget. He must spend the budget such that 2,500,000 x = 0. What property of addition tells us what the value of x must be?

inverse property of addition

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Technology

For the following exercises, use a graphing calculator to solve for x . Round the answers to the nearest hundredth.

0.5 ( 12.3 ) 2 48 x = 3 5

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( 0.25 0.75 ) 2 x 7.2 = 9.9

68.4

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Extensions

If a whole number is not a natural number, what must the number be?

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Determine whether the statement is true or false: The multiplicative inverse of a rational number is also rational.

true

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Determine whether the statement is true or false: The product of a rational and irrational number is always irrational.

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Determine whether the simplified expression is rational or irrational: −18 4 ( 5 ) ( −1 ) .

irrational

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Determine whether the simplified expression is rational or irrational: −16 + 4 ( 5 ) + 5 .

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The division of two whole numbers will always result in what type of number?

rational

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What property of real numbers would simplify the following expression: 4 + 7 ( x 1 ) ?

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Questions & Answers

the diagram of the digestive system
Assiatu Reply
allimentary cannel
Ogenrwot
How does twins formed
William Reply
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is genetics
Josephine Reply
Genetics is the study of heredity
Misack
how does twins formed?
Misack
What is manual
Hassan Reply
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
Joseph Reply
what is biology
Yousuf Reply
the study of living organisms and their interactions with one another and their environments
AI-Robot
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
Joseph Reply
what is the blood cells
Shaker Reply
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
Abdullahi Reply
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
What is classification
ISCONT Reply
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
Kenna Reply
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Condoleezza Reply
what is cell divisoin?
Aron Reply
Diversity of living thing
ISCONT
what is cell division
Aron Reply
Cell division is the process by which a single cell divides into two or more daughter cells. It is a fundamental process in all living organisms and is essential for growth, development, and reproduction. Cell division can occur through either mitosis or meiosis.
AI-Robot
What is life?
Allison Reply
life is defined as any system capable of performing functions such as eating, metabolizing,excreting,breathing,moving,Growing,reproducing,and responding to external stimuli.
Mohamed
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Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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