<< Chapter < Page Chapter >> Page >

( 11 a + 3 ) 18 a = −4

Got questions? Get instant answers now!

4 z 2 z ( 1 + 4 ) = 36

−6

Got questions? Get instant answers now!

4 y ( 7 2 ) 2 = −200

Got questions? Get instant answers now!

( 2 x ) 2 + 1 = −3

± 1

Got questions? Get instant answers now!

8 ( 2 + 4 ) 15 b = b

Got questions? Get instant answers now!

1 4 ( 8 w 4 2 ) = 0

2

Got questions? Get instant answers now!

For the following exercises, simplify the expression.

2 y ( 4 ) 2 y 11

−14 y 11

Got questions? Get instant answers now!

a 2 3 ( 64 ) 12 a ÷ 6

Got questions? Get instant answers now!

8 b 4 b ( 3 ) + 1

−4 b + 1

Got questions? Get instant answers now!

5 l ÷ 3 l × ( 9 6 )

Got questions? Get instant answers now!

7 z 3 + z × 6 2

43 z 3

Got questions? Get instant answers now!

4 × 3 + 18 x ÷ 9 12

Got questions? Get instant answers now!

9 ( y + 8 ) 27

9 y + 45

Got questions? Get instant answers now!

6 + 12 b 3 × 6 b

−6 b + 6

Got questions? Get instant answers now!

( 4 9 ) 2 × 27 x

16 x 3

Got questions? Get instant answers now!

8 ( 3 m ) + 1 ( 8 )

Got questions? Get instant answers now!

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

9 x

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

How much money does Fred keep?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

( 0.25 0.75 ) 2 x 7.2 = 9.9

68.4

Got questions? Get instant answers now!

Extensions

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

Got questions? Get instant answers now!

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

true

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

irrational

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

rational

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Questions & Answers

write down the polynomial function with root 1/3,2,-3 with solution
Gift Reply
if A and B are subspaces of V prove that (A+B)/B=A/(A-B)
Pream Reply
write down the value of each of the following in surd form a)cos(-65°) b)sin(-180°)c)tan(225°)d)tan(135°)
Oroke Reply
Prove that (sinA/1-cosA - 1-cosA/sinA) (cosA/1-sinA - 1-sinA/cosA) = 4
kiruba Reply
what is the answer to dividing negative index
Morosi Reply
In a triangle ABC prove that. (b+c)cosA+(c+a)cosB+(a+b)cisC=a+b+c.
Shivam Reply
give me the waec 2019 questions
Aaron Reply
the polar co-ordinate of the point (-1, -1)
Sumit Reply
prove the identites sin x ( 1+ tan x )+ cos x ( 1+ cot x )= sec x + cosec x
Rockstar Reply
tanh`(x-iy) =A+iB, find A and B
Pankaj Reply
B=Ai-itan(hx-hiy)
Rukmini
what is the addition of 101011 with 101010
Branded Reply
If those numbers are binary, it's 1010101. If they are base 10, it's 202021.
Jack
extra power 4 minus 5 x cube + 7 x square minus 5 x + 1 equal to zero
archana Reply
the gradient function of a curve is 2x+4 and the curve passes through point (1,4) find the equation of the curve
Kc Reply
1+cos²A/cos²A=2cosec²A-1
Ramesh Reply
test for convergence the series 1+x/2+2!/9x3
success Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask