# 1.1 Real numbers: algebra essentials  (Page 10/35)

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$4y+8=2y$

$-4$

$\left(11a+3\right)-18a=-4$

$4z-2z\left(1+4\right)=36$

$-6$

$4y{\left(7-2\right)}^{2}=-200$

$-{\left(2x\right)}^{2}+1=-3$

$±1$

$8\left(2+4\right)-15b=b$

$2\left(11c-4\right)=36$

2

$4\left(3-1\right)x=4$

$\frac{1}{4}\left(8w-{4}^{2}\right)=0$

2

For the following exercises, simplify the expression.

$4x+x\left(13-7\right)$

$2y-{\left(4\right)}^{2}y-11$

$-14y-11$

$\frac{a}{{2}^{3}}\left(64\right)-12a÷6$

$8b-4b\left(3\right)+1$

$-4b+1$

$5l÷3l\text{\hspace{0.17em}}×\text{\hspace{0.17em}}\left(9-6\right)$

$7z-3+z\text{\hspace{0.17em}}×\text{\hspace{0.17em}}{6}^{2}$

$43z-3$

$4\text{\hspace{0.17em}}×\text{\hspace{0.17em}}3+18x÷9-12$

$9\left(y+8\right)-27$

$9y+45$

$\left(\frac{9}{6}t-4\right)2$

$6+12b-3\text{\hspace{0.17em}}×\text{\hspace{0.17em}}6b$

$-6b+6$

$18y-2\left(1+7y\right)$

${\left(\frac{4}{9}\right)}^{2}\text{\hspace{0.17em}}×\text{\hspace{0.17em}}27x$

$\frac{16x}{3}$

$8\left(3-m\right)+1\left(-8\right)$

$9x+4x\left(2+3\right)-4\left(2x+3x\right)$

$9x$

${5}^{2}-4\left(3x\right)$

## 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. $\frac{1}{2}\left(40-10\right)+5$ How much money does Fred keep? 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 $\text{\hspace{0.17em}}\pi .\text{\hspace{0.17em}}$ Is the circumference of a quarter a whole number, a rational number, or an irrational number? irrational number 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? For the following exercises, consider this scenario: There is a mound of $\text{\hspace{0.17em}}g\text{\hspace{0.17em}}$ 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. $g+400-2\left(600\right)=1200$ Solve for g . 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 $\text{\hspace{0.17em}}2,500,000-x=0.\text{\hspace{0.17em}}$ What property of addition tells us what the value of x must be?

## Technology

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

$0.5{\left(12.3\right)}^{2}-48x=\frac{3}{5}$

${\left(0.25-0.75\right)}^{2}x-7.2=9.9$

68.4

## Extensions

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

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

true

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

Determine whether the simplified expression is rational or irrational: $\text{\hspace{0.17em}}\sqrt{-18-4\left(5\right)\left(-1\right)}.$

irrational

Determine whether the simplified expression is rational or irrational: $\text{\hspace{0.17em}}\sqrt{-16+4\left(5\right)+5}.$

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

rational

What property of real numbers would simplify the following expression: $\text{\hspace{0.17em}}4+7\left(x-1\right)?$

what is math number
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Need help solving this problem (2/7)^-2
x+2y-z=7
Sidiki
what is the coefficient of -4×
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
An investment account was opened with an initial deposit of \$9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
12, 17, 22.... 25th term
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Atone
hi
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
hi vedant can u help me with some assignments
Solomon
find the 15th term of the geometric sequince whose first is 18 and last term of 387
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
If f(x) = x-2 then, f(3) when 5f(x+1) 5((3-2)+1) 5(1+1) 5(2) 10
Augustine
how do they get the third part x = (32)5/4
make 5/4 into a mixed number, make that a decimal, and then multiply 32 by the decimal 5/4 turns out to be
AJ
how
Sheref
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
hi
Ayuba
Hello
opoku
hi
Ali
greetings from Iran
Ali
salut. from Algeria
Bach
hi
Nharnhar