Chapter 1

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$(24 \div 6) \div 2=24 \div(6 \div 2)$$

Let \(x\) represent the number. Express each sentence as a single algebraic expression. Then simplify the expression. Multiply a number by \(5 .\) Add 8 to this product. Subtract this sum from the number.

In Exercises \(77-96,\) simplify each algebraic expression. $$-(2 y-5)$$

Writing about mathematics will help you to learn mathematics. For all writing exercises in this book, use complete sentences to respond to the questions. Some writing exercises can be answered in a sentence; others require a paragraph or two. You can decide how much you need to write as long as your writing clearly and directly answers the question in the exercise. Standard references such as a dictionary and a thesaurus should be helpful. What is an equation?

Determine whether natural numbers, whole numbers, integers, rational numbers, or all real numbers are appropriate for each situation. The number of pets a person has

Write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. The quotient of \(-2\) and a number, subtracted from the quotient of \(-5\) and the number

Determine whether the given number is a solution of the equation. $$w-\frac{2}{3}=\frac{3}{4} ; 1 \frac{5}{12}$$

Let \(x\) represent the number. Express each sentence as a single algebraic expression. Then simplify the expression. Multiply a number by 3. Add 9 to this product. Subtract this sum from the number.

In Exercises \(77-96,\) simplify each algebraic expression. $$-(3 y-1)$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$2 x+5=5 x+2$$

Writing about mathematics will help you to learn mathematics. For all writing exercises in this book, use complete sentences to respond to the questions. Some writing exercises can be answered in a sentence; others require a paragraph or two. You can decide how much you need to write as long as your writing clearly and directly answers the question in the exercise. Standard references such as a dictionary and a thesaurus should be helpful. How do you tell the difference between an algebraic expression and an equation?

Determine whether natural numbers, whole numbers, integers, rational numbers, or all real numbers are appropriate for each situation. The number of siblings a person has

Write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. The quotient of \(-7\) and a number, subtracted from the quotient of \(-12\) and the number

Determine whether the given number is a solution of the equation. $$w-\frac{3}{4}=\frac{7}{4} ; 2 \frac{1}{2}$$

Let \(x\) represent the number. Express each sentence as a single algebraic expression. Then simplify the expression. Cube a number. Subtract 4 from this exponential expression. Multiply this difference by 5 .

In Exercises \(77-96,\) simplify each algebraic expression. $$4(2 y-3)-(7 y+2)$$

The table shows the record low temperatures for five U.S. states. \begin{array}{|c|c|c|}\hline \text { State } & \text { Record Low ( \(^{\circ} \mathrm{F}\) ) } & \text { Date } \\\\\hline \text { Florida } & -2 & \text { Feb. 13, 1899 } \\\\\hline \text { Georgia } & -17 & \text { Jan. 27, 1940 } \\\\\hline \text { Hawaii } & 12 & \text { May 17, 1979 } \\\\\hline \text { Louisiana } & -16 & \text { Feb. 13, 1899 } \\\\\hline \text { Rhode Island } & -25 & \text { Feb. 5, 1996 } \\\\\hline\end{array} a. Graph the five record low temperatures on a number line. b. Write the names of the states in order from the coldest record low to the warmest record low.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(a+(b c)=(a+b)(a+c) ;\) in words, addition can be distributed over multiplication.

Writing about mathematics will help you to learn mathematics. For all writing exercises in this book, use complete sentences to respond to the questions. Some writing exercises can be answered in a sentence; others require a paragraph or two. You can decide how much you need to write as long as your writing clearly and directly answers the question in the exercise. Standard references such as a dictionary and a thesaurus should be helpful. How do you determine whether a given number is a solution of an equation?

The peak of Mount Kilimanjaro, the highest point in Africa, is \(19,321\) feet above sea level. Qattara Depression, Egypt, one of the lowest points in Africa, is 436 feet below sea level. What is the difference in elevation between the peak of Mount Kilimanjaro and the Qattara Depression?

Determine whether the given number is a solution of the equation. $$20-\frac{1}{3} z=\frac{1}{2} z ; 12$$

Let \(x\) represent the number. Express each sentence as a single algebraic expression. Then simplify the expression. Cube a number. Subtract 6 from this exponential expression. Multiply this difference by 4

In Exercises \(77-96,\) simplify each algebraic expression. $$5(3 y-1)-(14 y-2)$$

The table shows the record low temperatures for five U.S. states. \begin{array}{|c|c|c|}\hline \text { State } & \text { Record Low ( \(^{\circ} \mathrm{F}\) ) } & \text { Date } \\\\\hline \text { Virginia } & -30 & \text { Jan. } 22,1985 \\\\\hline \text { Washington } & -48 & \text { Dec. } 30,1968 \\\\\hline \text { West Virginia } & -37 & \text { Dec. } 30,1917 \\\\\hline \text { Wisconsin } & -55 & \text { Feb. } 4,1996 \\\\\hline \text { Wyoming } & -66 & \text { Feb. } 9,1933 \\\\\hline\end{array} a. Graph the five record low temperatures on a number line. b. Write the names of the states in order from the coldest record low to the warmest record low.

Writing about mathematics will help you to learn mathematics. For all writing exercises in this book, use complete sentences to respond to the questions. Some writing exercises can be answered in a sentence; others require a paragraph or two. You can decide how much you need to write as long as your writing clearly and directly answers the question in the exercise. Standard references such as a dictionary and a thesaurus should be helpful. What is a mathematical model?

The peak of Mount Whitney is \(14,494\) feet above sea level. Mount Whitney can be seen directly above Death Valley, which is 282 feet below sea level. What is the difference in elevation between these geographic locations?

Determine whether the given number is a solution of the equation. $$12-\frac{1}{4} z=\frac{1}{2} z ; 20$$

In Exercises \(97-108,\) determine whether the given number is a solution of the equation. $$4 x=2 x-10 ;-5$$

What is a set?

Will help you prepare for the material covered in the next section. In each exercise, write an integer that is the result of the given situation. You earn \(\$ 150\), but then you misplace \(\$ 90\).

Determine whether the given number is a solution of the equation. $$\frac{2}{9} y+\frac{1}{3} y=\frac{3}{7} ; \frac{27}{35}$$

What are the natural numbers?

Will help you prepare for the material covered in the next section. In each exercise, write an integer that is the result of the given situation. You lose \(\$ 50\) and then you misplace \(\$ 10\).

Writing about mathematics will help you to learn mathematics. For all writing exercises in this book, use complete sentences to respond to the questions. Some writing exercises can be answered in a sentence; others require a paragraph or two. You can decide how much you need to write as long as your writing clearly and directly answers the question in the exercise. Standard references such as a dictionary and a thesaurus should be helpful. In Exercises \(87-88,\) we used the formula \(H=0.8(200-A)\) to find a bowler's handicap, \(H,\) where the variable \(A\) represents the bowler's average score. Describe what happens to the handicap when the average score is \(200 .\)

Determine whether the given number is a solution of the equation. $$\frac{2}{3} y+\frac{5}{6} y=2 ; 1 \frac{1}{3}$$

In Exercises \(97-108,\) determine whether the given number is a solution of the equation. $$-7 y+18=-10 y+6 ;-4$$

What are the whole numbers?

Will help you prepare for the material covered in the next section. In each exercise, write an integer that is the result of the given situation. The temperature is 30 degrees, and then it drops by 35 degrees.

Determine whether the given number is a solution of the equation. $$\frac{1}{3}(x-2)=\frac{1}{5}(x+4)+3 ; 26$$

In Exercises \(97-108,\) determine whether the given number is a solution of the equation. $$-4 y+21=-7 y+15 ;-2$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I'm solving a problem that requires me to determine if 5 is a solution of \(4 x+7\)

Determine whether the given number is a solution of the equation. $$\frac{1}{2}(x-2)+3=\frac{3}{8}(3 x-4) ; 4$$

In Palo Alto, California, a government agency ordered computer-related companies to contribute to a pool of money to clean up underground water supplies. (The companies had stored toxic chemicals in leaking underground containers.) The mathematical model $$ C=\frac{200 x}{100-x} $$ describes the cost, \(C,\) in tens of thousands of dollars, for removing \(x\) percent of the contaminants. Use this formula to solve. a. Find the cost, in tens of thousands of dollars, for removing \(50 \%\) of the contaminants. b. Find the cost, in tens of thousands of dollars, for removing \(80 \%\) of the contaminants. c. Describe what is happening to the cost of the cleanup as the percentage of contaminant removed increases.

In Exercises \(97-108,\) determine whether the given number is a solution of the equation. $$5(w+3)=2 w-21 ;-10$$

How does the set of integers differ from the set of whole numbers?

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. The model \(T=0.15 n+2.72\) describes the average movie ticket price, \(T, n\) years after \(1980,\) so I can use it to estimate the average movie ticket price in 1980 .

Determine whether the given number is a solution of the equation. $$(y \div 6)+\frac{2}{3}=(y \div 2)-\frac{7}{9} ; 4 \frac{1}{3}$$

In Palo Alto, California, a government agency ordered computer-related companies to contribute to a pool of money to clean up underground water supplies. (The companies had stored toxic chemicals in leaking underground containers.) The mathematical model $$ C=\frac{200 x}{100-x} $$ describes the cost, \(C,\) in tens of thousands of dollars, for removing \(x\) percent of the contaminants. Use this formula to solve. a. Find the cost, in tens of thousands of dollars, for removing \(60 \%\) of the contaminants. b. Find the cost, in tens of thousands of dollars, for removing \(90 \%\) of the contaminants. c. Describe what is happening to the cost of the cleanup as the percentage of contaminants removed increases.

From here on, each exercise set will contain three review exercises. It is essential to review previously covered topics to improve your understanding of the topics and to help maintain your mastery of the material. If you are not certain how to solve a review exercise, turn to the section and the worked example given in parentheses at the end of each exercise. Consider the set $$\\{-6,-\pi, 0,0, \overline{7}, \sqrt{3}, \sqrt{4}\\}$$ List all numbers from the set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. (Section 1.3 Example 5 )

Describe how to graph a number on the number line.