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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

Why is b in the answer
Dahsolar Reply
how do you work it out?
Brad Reply
answer
Ernest
heheheehe
Nitin
(Pcos∅+qsin∅)/(pcos∅-psin∅)
John Reply
how to do that?
Rosemary Reply
what is it about?
Amoah
how to answer the activity
Chabelita Reply
how to solve the activity
Chabelita
solve for X,,4^X-6(2^)-16=0
Alieu Reply
x4xminus 2
Lominate
sobhan Singh jina uniwarcity tignomatry ka long answers tile questions
harish Reply
t he silly nut company makes two mixtures of nuts: mixture a and mixture b. a pound of mixture a contains 12 oz of peanuts, 3 oz of almonds and 1 oz of cashews and sells for $4. a pound of mixture b contains 12 oz of peanuts, 2 oz of almonds and 2 oz of cashews and sells for $5. the company has 1080
ZAHRO Reply
If  , , are the roots of the equation 3 2 0, x px qx r     Find the value of 1  .
Swetha Reply
Parts of a pole were painted red, blue and yellow. 3/5 of the pole was red and 7/8 was painted blue. What part was painted yellow?
Patrick Reply
Parts of the pole was painted red, blue and yellow. 3 /5 of the pole was red and 7 /8 was painted blue. What part was painted yellow?
Patrick
how I can simplify algebraic expressions
Katleho Reply
Lairene and Mae are joking that their combined ages equal Sam’s age. If Lairene is twice Mae’s age and Sam is 69 yrs old, what are Lairene’s and Mae’s ages?
Mary Reply
23yrs
Yeboah
lairenea's age is 23yrs
ACKA
hy
Katleho
Ello everyone
Katleho
Laurene is 46 yrs and Mae is 23 is
Solomon
hey people
christopher
age does not matter
christopher
solve for X, 4^x-6(2*)-16=0
Alieu
prove`x^3-3x-2cosA=0 (-π<A<=π
Mayank Reply
create a lesson plan about this lesson
Rose Reply
Excusme but what are you wrot?

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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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