Chapter 1

In Exercises \(89-92,\) express each sentence as a single numerical expression. Then use the order of operations to simplify the expression. Subtract 11 from \(9 .\) Multiply this difference by \(2 .\) Raise this product to the fourth power.

Simplify each algebraic expression. $$-4(-3 x+2)$$

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. If \(x\) represents the number, explain the difference between translating the following phrases: a number decreased by 5 a number subtracted from 5 .

Determine whether each statement “makes sense” or “does not make sense” and explain your reasoning. The commutative, associative, and distributive properties remind me of the rules of a game.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{3}{4}+\left(-\frac{3}{5}\right)=-\frac{3}{20}$$

Determine whether the given number is a solution of the equation. $$\frac{5}{3} x=30 ; 18$$

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

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 each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The sum of zero and a negative number is always a negative number.

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

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

In Exercises \(93-96\), 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.

Simplify each algebraic expression. $$-(3 y-1)$$

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

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

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?

In Exercises \(93-96\), 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 \(5 .\)

Simplify each algebraic expression. $$4(2 y-3)-(7 y+2)$$

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 determine whether a given number is a solution of an equation?

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

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?

Simplify each algebraic expression. $$5(3 y-1)-(14 y-2)$$

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. What is a mathematical model?

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

What is a set?

Determine whether the given number is a solution of the equation. $$4 x=2 x-10 ;-5$$

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 \(\$ 90\).

What are the natural numbers?

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

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 .

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 \(\$ 10\).

What are the whole numbers?

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

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. As I read this book, I write questions in the margins that I might ask in class.

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. $$\frac{1}{2}(x-2)+3=\frac{3}{8}(3 x-4) ; 4$$

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 Exercises \(101-102\). 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.

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

Determine whether the given number is a solution of the equation. $$5(w+3)=2 w-21 ;-10$$

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 .

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 Exercises \(101-102\). 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.

Describe how to graph a number on the number line.

Determine whether the given number is a solution of the equation. $$6(w+2)=4 w-10 ;-9$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. Because there are four quarters in a dollar, I can use the formula \(q=4 d\) to determine the number of quarters, \(q,\) in \(d\) dollars.

Consider the set $$\\{-6,-\pi, 0,0, \overline{7}, \sqrt{3}, \sqrt{4}\\}$$ List all numbers from the set that are a. natural numbers, whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. (Section 1.3 Example 5 )

What is a rational number?