Chapter 1

Write a problem that can be solved by finding the sum of at least three numbers, some positive and some negative. Then explain how to solve the problem.

Simplify each algebraic expression by removing parentheses and brackets. $$6-5[8-(2 y-4)]$$

In Exercises \(77-96,\) simplify each algebraic expression. $$12 b-13 b$$

What does it mean to simplify an algebraic expression?

Find the value of each expression. $$-|-8-(-2)|-(-6)$$

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{3}{2}-\frac{2}{3}$$

Without a calculator, you can add numbers using a number line, using absolute value, or using gains and losses. Which method do you find most helpful? Why is this so?

Simplify each algebraic expression by removing parentheses and brackets. $$2\left(3 x^{2}-5\right)-\left[4\left(2 x^{2}-1\right)+3\right]$$

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

An algebra student incorrectly used the distributive property and wrote \(3(5 x+7)=15 x+7 .\) If you were that student's teacher, what would you say to help the student avoid this kind of error?

Determine whether natural numbers, whole numbers, integers, rational numbers, or all real numbers are appropriate for each situation. Shoe sizes of students on campus

A bowler's handicap, \(H,\) is often found using the following formula: $$H=0.8(200-A)$$ A bowler's final score for a game is the score for that game increased by the handicap. a. If your average bowling score is \(145,\) what is your handicap? b. What would your final score be if you bowled 120 in a game?

Find the value of each expression. $$\frac{5}{8}-\left(\frac{1}{2}-\frac{3}{4}\right)$$

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{7}{10}-\frac{3}{16}$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. It takes me too much time to add real numbers with a number line.

Simplify each algebraic expression by removing parentheses and brackets. $$4\left(6 x^{2}-3\right)-\left[2\left(5 x^{2}-1\right)+1\right]$$

In Exercises \(77-96,\) simplify each algebraic expression. $$-y+9 y$$

You can transpose the letters in the word "conversation" to form the phrase "voices rant on." From "total abstainers" we can form "sit not at ale bars." What two algebraic properties do each of these transpositions (called anagrams) remind you of? Explain your answer.

Determine whether natural numbers, whole numbers, integers, rational numbers, or all real numbers are appropriate for each situation. Recorded heights of students on campus

A bowler's handicap, \(H,\) is often found using the following formula: $$H=0.8(200-A)$$ A bowler's final score for a game is the score for that game increased by the handicap. a. If your average bowling score is \(165,\) what is your handicap? b. What would your final score be if you bowled 140 in a game?

Find the value of each expression. $$\frac{9}{10}-\left(\frac{1}{4}-\frac{7}{10}\right)$$

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{7}{30}-\frac{5}{24}$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I found the sum of \(-13\) and 4 by thinking of temperatures above and below zero: If it's 13 below zero and the temperature rises 4 degrees, the new temperature will be 9 below zero, so \(-13+4=-9\)

Express each sentence as a single numerical expression. Then use the order of operations to simplify the expression. Cube \(-2 .\) Subtract this exponential expression from \(-10\)

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

Determine whether natural numbers, whole numbers, integers, rational numbers, or all real numbers are appropriate for each situation. Temperatures in weather reports

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 variable?

Find the value of each expression. $$|-9-(-3+7)|-|-17-(-2)|$$

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$3 \frac{3}{4}-2 \frac{1}{3}$$

Express each sentence as a single numerical expression. Then use the order of operations to simplify the expression Cube \(-5 .\) Subtract this exponential expression from \(-100 .\)

In Exercises \(77-96,\) simplify each algebraic expression. $$-3(4 x-5)$$

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 algebraic expression?

Determine whether natural numbers, whole numbers, integers, rational numbers, or all real numbers are appropriate for each situation. Class sizes of algebra courses

Find the value of each expression. $$|24-(-16)|-|-51-(-31+2)|$$

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$3 \frac{2}{3}-2 \frac{1}{2}$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. Without adding numbers, I can see that the sum of \(-227\) and 319 is greater than the sum of 227 and \(-319\)

Express each sentence as a single numerical expression. Then use the order of operations to simplify the expression Subtract 10 from \(7 .\) Multiply this difference by \(2 .\) Square this product.

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

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. Explain how to evaluate \(2+5 x\) for \(x=3\)

Determine whether natural numbers, whole numbers, integers, rational numbers, or all real numbers are appropriate for each situation. Values of \(d\) given by the formula \(d=\sqrt{1.5 h},\) where \(d\) is the distance, in miles, that you can see to the horizon from a height of \(h\) feet

Write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. The difference between 6 times a number and \(-5\) times the number

Determine whether the given number is a solution of the equation. $$\frac{7}{2} x=28 ; 8$$

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

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.

In Exercises \(77-96,\) 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.

Values of \(d\) given by the formula \(d=\sqrt{1.5 h},\) where \(d\) is the distance, in miles, that you can see to the horizon from a height of \(h\) feet Values of \(C\) given by the formula \(C=2 \pi r\), where \(C\) is the circumference of a circle with radius \(r\)

Write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. The difference between 9 times a number and \(-4\) times the number

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