Chapter 1

Explain how to find the terms of the algebraic expression \(5 x-2 y-7\)

Translate from English to an algebraic expression or equation, whichever is appropriate. Let the variable \(x\) represent the number. The product of \(\frac{3}{4}\) and a number, increased by \(9,\) is 2 less than the number.

Insert parentheses in each expression so that the resulting value is 45 $$2 \cdot 3+3 \cdot 5$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Irrational numbers cannot be negative.

In Exercises \(109-116\), write a numerical expression for each phrase. Then simplify the numerical expression by performing the given operations. The difference between \(-6\) and the quotient of 12 and \(-4\)

Write a problem that can be solved by finding the difference between two numbers. At least one of the numbers should be negative. Then explain how to solve the problem.

Perform the indicated operation. Write the answer as an algebraic expression. $$\frac{3}{4} \cdot \frac{a}{5}$$

Insert parentheses in each expression so that the resulting value is 45 $$2 \cdot 5-\frac{1}{2} \cdot 10 \cdot 9$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Some real numbers are not rational numbers.

In Exercises \(109-116\), write a numerical expression for each phrase. Then simplify the numerical expression by performing the given operations. The difference between \(-11\) and the quotient of 20 and \(-5\)

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I already knew how to add positive and negative numbers, so there was not that much new to learn when it came to subtracting them.

Perform the indicated operation. Write the answer as an algebraic expression. $$\frac{2}{3} \div \frac{a}{7}$$

Simplify: \(-8-2-(-5)+11 .\) (Section \(1.6,\) Example 3 )

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Some integers are not rational numbers.

In Exercises \(117-118\), use the formula \(C=\frac{5}{4}(F-32)\) to express each Fahrenheit temperature, \(F,\) as its equivalent Celsius temperature, \(C\). $$-22^{\circ} \mathrm{F}$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I can find the closing price of stock PQR on Wednesday by subtracting the change in price, \(-1.23,\) from the closing price on Thursday, 47.19 .

Perform the indicated operation. Write the answer as an algebraic expression. $$\frac{11}{x}+\frac{9}{x}$$

Multiply: \(-4(-1)(-3)(2) .\) (Section 1.7 , Example 2)

Write each phrase as an algebraic expression. a loss of \(\frac{1}{3}\) of an investment of \(d\) dollars

In Exercises \(117-118\), use the formula \(C=\frac{5}{4}(F-32)\) to express each Fahrenheit temperature, \(F,\) as its equivalent Celsius temperature, \(C\). $$-31^{\circ} \mathrm{F}$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I found the variation in elevation between two heights by taking the difference between the high point and the low point.

Perform the indicated operation. Write the answer as an algebraic expression. $$\frac{10}{y}-\frac{6}{y}$$

Give an example of a real number that is not an irrational number. (Section \(1.3,\) Example 5 ).

Write each phrase as an algebraic expression. a loss of half of an investment of \(d\) dollars

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I found the variation in U.S. temperature by subtracting the record low temperature, a negative number, from the record high temperature, a positive number.

Perform the indicated operations. Begin by performing operations in parentheses. $$\left(\frac{1}{2}-\frac{1}{3}\right) \div \frac{5}{8}$$

In each exercise, determine whether the given number is a solution of the equation. $$-\frac{1}{2}=x-\frac{2}{3} ; \frac{1}{6}$$

Use a calculator to find a decimal approximation for each irrational number, correct to three decimal places. Between which two integers should you graph each of these numbers on the number line? $$\sqrt{3}$$

If \(a\) and \(b\) are negative numbers, then \(a-b\) is sometimes a negative number.

Perform the indicated operations. Begin by performing operations in parentheses. $$\left(\frac{1}{2}+\frac{1}{4}\right) \div\left(\frac{1}{2}+\frac{1}{3}\right)$$

In each exercise, determine whether the given number is a solution of the equation. $$5 y+3-4 y-8=15 ; 20$$

Use a calculator to find a decimal approximation for each irrational number, correct to three decimal places. Between which two integers should you graph each of these numbers on the number line? $$-\sqrt{12}$$

Determine whether the given number is a solution of the equation. $$\frac{1}{5}(x+2)=\frac{1}{2}\left(x-\frac{1}{5}\right) ; \frac{5}{8}$$

In each exercise, determine whether the given number is a solution of the equation. $$4 x+2=3(x-6)+8 ;-11$$

Use a calculator to find a decimal approximation for each irrational number, correct to three decimal places. Between which two integers should you graph each of these numbers on the number line? $$1-\sqrt{2}$$

In Exercises \(120-123\), use a calculator to find a decimal approximation for each irrational number, correct to three decimal places. Between which two integers should you graph each of these numbers on the number line? \(1-\sqrt{2}\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The difference between 0 and a negative number is always a positive number.

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

Explain how to multiply two real numbers. Provide examples with your explanation.

Use a calculator to find a decimal approximation for each irrational number, correct to three decimal places. Between which two integers should you graph each of these numbers on the number line? $$2-\sqrt{5}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(|a-b|=|b-a|\)

The formula $$C=\frac{5}{9}(F-32)$$ expresses the relationship between Fahrenheit temperature, \(F\) and Celsius temperature, \(C .\) In Exercises \(123-124,\) use the formula to convert the given Fahrenheit temperature to its equivalent temperature on the Celsius scale. $$68^{\circ} \mathrm{F}$$

Evaluate both expressions for \(x=4 .\) What do you observe? $$3(x+5) ; 3 x+15$$

Explain how to determine the sign of a product that involves more than two numbers.

The formula $$C=\frac{5}{9}(F-32)$$ expresses the relationship between Fahrenheit temperature, \(F\) and Celsius temperature, \(C .\) In Exercises \(123-124,\) use the formula to convert the given Fahrenheit temperature to its equivalent temperature on the Celsius scale. $$41^{\circ} \mathrm{F}$$

Explain how to find the multiplicative inverse of a number.

The maximum heart rate, in beats per minute, that you should achieve during exercise is 220 minus your age: CAN'T COPY THE GRAPH The bar graph shows the target heart rate ranges for four types of exercise goals. The lower and upper limits of these ranges are fractions of the maximum heart rate, \(220-a\). CAN'T COPY THE GRAPH If your exercise goal is to improve cardiovascular conditioning, the graph shows the following range for target heart rate, \(H,\) in beats per minute: Lower limit of range $$H=\frac{7}{10}(220-a)$$ Upper limit of range $$H=\frac{4}{5}(220-a)$$ a. What is the lower limit of the heart range, in beats per minute, for a 20 -year-old with this exercise goal? b. What is the upper limit of the heart range, in beats per minute, for a 20 -year-old with this exercise goal?

Why is it that 0 has no multiplicative inverse?

The maximum heart rate, in beats per minute, that you should achieve during exercise is 220 minus your age: CAN'T COPY THE GRAPH The bar graph shows the target heart rate ranges for four types of exercise goals. The lower and upper limits of these ranges are fractions of the maximum heart rate, \(220-a\). CAN'T COPY THE GRAPH If your exercise goal is to improve overall health, the graph on the previous page shows the following range for target heart rate, \(H,\) in beats per minute: Lower limit of range $$H=\frac{1}{2}(220-a)$$ Upper limit of range $$H=\frac{3}{5}(220-a)$$ a. What is the lower limit of the heart range, in beats per minute, for a 30 -year-old with this exercise goal? b. What is the upper limit of the heart range, in beats per minute, for a 30 -year-old with this exercise goal?

Explain how to divide real numbers.