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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

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
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what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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