# 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: $\text{\hspace{0.17em}}4+7\left(x-1\right)?$

how do I set up the problem?
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
Abdullahi
hi mam
Mark
find the value of 2x=32
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
yes i wantt to review
Mark
use the y -intercept and slope to sketch the graph of the equation y=6x
how do we prove the quadratic formular
Darius
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
thank you help me with how to prove the quadratic equation
Seidu
may God blessed u for that. Please I want u to help me in sets.
Opoku
what is math number
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
can you teacch how to solve that🙏
Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Brenna
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 By Ruben Schinkel By By Richley Crapo By Richley Crapo By Brooke Delaney By Brooke Delaney By Dionne Mahaffey By Madison Christian By Rhodes By OpenStax By OpenStax By OpenStax