Chapter 1

Simplify: \(\frac{1}{4}-6(2+8) \div\left(-\frac{1}{3}\right)\left(-\frac{1}{9}\right)\)

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

Write a numerical expression for each phrase. Then simplify the numerical expression by performing the given operations. The quotient of \(-25\) and the sum of \(-21\) and 16

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.

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.

In Exercises \(115-116,\) 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.

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 \(-4\)

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

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.

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 \(-5\)

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

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

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

Use the formula \(C=5(F-32)\) to express each Fahrenheit temperature, \(F,\) as its equivalent Celsius temperature, \(C\). $$-22^{\circ} \mathrm{F}$$

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

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.

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

Use the formula \(C=5(F-32)\) to express each Fahrenheit temperature, \(F,\) as its equivalent Celsius temperature, \(C\). $$-31^{\circ} \mathrm{F}$$

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

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.

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

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

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If \(a\) and \(b\) are negative numbers, then \(a-b\) is sometimes a negative number.

Exercises \(120-122\) will help you prepare for the material covered in the first section of the next chapter. 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? $$\sqrt{3}$$

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

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(7-(-2)=5\)

Exercises \(120-122\) will help you prepare for the material covered in the first section of the next chapter. In each exercise, determine whether the given number is a solution of the equation. $$5 y+3-4 y-8=15 ; 20$$

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

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.

Exercises \(120-122\) will help you prepare for the material covered in the first section of the next chapter. 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? $$1-\sqrt{2}$$

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

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

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? $$2-\sqrt{5}$$

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

Explain how to find the multiplicative inverse of a number.

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?

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.

Order the expressions \(|x-y|,|x|-|y|,\) and \(|x+y|\) from least to greatest for \(x=-6\) and \(y=-8\).

Why is division by zero undefined?

Explain how to simplify an algebraic expression in which a negative sign precedes parentheses.

Determine whether 2 is a solution of \(13 x+3=3(5 x-1)\) (Section \(1.1,\) Example 4 )

Explain how to convert a mixed number to an improper fraction and give an example.