Chapter 1

Write each phrase as an algebraic expression. Let \(x\) represent the unknown number. The quotient of a number and 9

Translate each phrase; then simplify. See Example 22. Find the sum of \(-49,-2,\) and 40 .

Write each algebraic expression described. The value of 7 nickels is \(5 \cdot 7\) cents. Likewise, the value of \(x\) nickels is \(5 x\) cents. If the money box in a drink machine contains \(x\) nickels, \(3 x\) dimes, and \((30 x-1)\) quarters, express their total value in cents as an algebraic expression.

Evaluate each expression. \(-4(3-9)\)

Write each phrase as an algebraic expression. Let \(x\) represent the unknown number. Three times a number, increased by 22

Solve. See Example 22. Suppose a deep-sea diver dives from the surface to 215 feet below the surface. He then dives down 16 more feet. Use positive and negative numbers to represent this situation. Then find the diver's present depth.

Write each algebraic expression described. In your own words, explain how to combine like terms.

Evaluate each expression. \(-7(-2)-3(-1)\)

The apparent magnitude of a star is the measure of its brightness as seen by someone on Earth. The smaller the apparent magnitude, the brighter the star. Below, the apparent magnitudes of some stars are listed. Use this table to answer Exercises 85 through \(90 .\) The apparent magnitude of the sun is -26.7 . The apparent magnitude of the star Arcturus is -0.04 . Write an inequality statement comparing the numbers -0.04 and -26.7 .

Mixed Practice Name the property illustrated by each true statement. See Examples 15 through 21. $$ -6 \cdot 1=-6 $$

Write each phrase as an algebraic expression. Let \(x\) represent the unknown number. Twice a number, decreased by 72

Solve. See Example 22. Suppose a diver dives from the surface to 248 meters below the surface and then swims up 8 meters, down 16 meters, down another 28 meters, and then up 32 meters. Use positive and negative numbers to represent this situation. Then find the diver's depth after these movements.

Write each algebraic expression described. Do like terms always contain the same numerical coefficients? Explain your answer.

Evaluate each expression. \(-8(-3)-4(-1)\)

The apparent magnitude of a star is the measure of its brightness as seen by someone on Earth. The smaller the apparent magnitude, the brighter the star. Below, the apparent magnitudes of some stars are listed. Use this table to answer. The apparent magnitude of Antares is 0.96 . The apparent magnitude of Spica is 0.98 . Write an inequality statement comparing the numbers 0.96 and 0.98 .

Translate each phrase to an algebraic expression. Use " \(x\) " to represent "a number." The sum of -5 and a number.

Write each sentence as an equation or inequality. Use \(x\) to represent any unknown number. One increased by two equals the quotient of nine and three.

Evaluate each expression. \(2^{2}-3[(2-8)-(-6-8)]\)

Translate each phrase to an algebraic expression. Use " \(x\) " to represent "a number." The difference of -3 and a number.

Write each sentence as an equation or inequality. Use \(x\) to represent any unknown number. Four subtracted from eight is equal to two squared.

Solve. See Example 22. On January \(2,1943,\) the temperature was \(-4^{\circ}\) at 7:30 a.m. in Spearfish, South Dakota. Incredibly, it got \(49^{\circ}\) warmer in the next 2 minutes. To what temperature did it rise by \(7: 32 ?\)

Evaluate each expression. \(3^{2}-2[(3-5)-(2-9)]\)

Fill in the table with the opposite (additive inverse), the reciprocal (multiplicative inverse), or the expression. Assume that the value of each expression is not 0. $$ \begin{array}{|c|c|c|} \hline & \text { 88. } \\ \hline \text { Expression } & -\frac{2}{3} \\ \hline \end{array} $$

Translate each phrase to an algebraic expression. Use " \(x\) " to represent "a number." Subtract a number from -20 .

Write each sentence as an equation or inequality. Use \(x\) to represent any unknown number. Three is not equal to four divided by two.

Solve. See Example 22. The lowest elevation on Earth is -411 meters (that is, 411 meters below sea level) at the Dead Sea. If you are standing 316 meters above the Dead Sea, what is your elevation? (Source: National Geographic Society)

Evaluate each expression. \(\frac{-6^{2}+4}{-2}\)

Translate each phrase to an algebraic expression. Use " \(x\) " to represent "a number." Add a number and -36 .

Write each sentence as an equation or inequality. Use \(x\) to represent any unknown number. The difference of sixteen and four is greater than ten.

Solve. See Example 22. The lowest elevation in Australia is -52 feet at Lake Eyre. If you are standing at a point 439 feet above Lake Eyre, what is your elevation? (Source: National Geographic Society)

Evaluate each expression. \(\frac{3^{2}+4}{5}\)

Write each sentence as an equation or inequality. Use \(x\) to represent any unknown number. The sum of 5 and a number is 20 .

Solve. See Example 22. During the PGA 2008 Wyndham Championship tournament, the winner, Carl Pettersson, had scores of \(-6,-9,-4,\) and \(-2 .\) What was his total score for the tournament? (Source: Professional Golfer's Association)

Evaluate each expression. \(\frac{-3-5^{2}}{2(-7)}\)

In your own words, explain how to find the absolute value of a number.

Fill in the table with the opposite (additive inverse), the reciprocal (multiplicative inverse), or the expression. Assume that the value of each expression is not 0. $$ \text { Reciprocal: } $$ $$ \frac{1}{2 x} $$

Write each sentence as an equation or inequality. Use \(x\) to represent any unknown number. Seven subtracted from a number is 0

Evaluate each expression. \(\frac{-2-4^{2}}{3(-6)}\)

Give an example of a real-life situation that can be described with integers but not with whole numbers.

Fill in the table with the opposite (additive inverse), the reciprocal (multiplicative inverse), or the expression. Assume that the value of each expression is not 0. $$ \text { Opposite: } $$ $$ 7 x $$

Write each sentence as an equation or inequality. Use \(x\) to represent any unknown number. The product of 7.6 and a number is 17 .

Solve. See Example 22. A negative net income results when a company spends more money than it brings in. Johnson Outdoors Inc. had the following quarterly net incomes during its 2009 fiscal year. (Source: Yahoo Finance) $$ \begin{array}{|c|c|} \hline \text { Quarter of Fiscal 2009 } & \text { Net Income (in millions) } \\\ \hline \text { First } & 2.5 \\ \hline \text { Second } & 9 \\ \hline \text { Third } & -14.2 \\ \hline \text { Fourth } & -4.2 \\ \hline \end{array} $$ What was the total net income for fiscal year \(2009 ?\)

Evaluate each expression. \(\frac{22+(3)(-2)^{2}}{-5-2}\)

Decide whether each statement is true or false. See the second Concept Check in this section. $$ \text { The opposite of }-\frac{a}{2} \text { is }-\frac{2}{a} \text { . } $$

Write each sentence as an equation or inequality. Use \(x\) to represent any unknown number. 9.1 times a number equals 4

LeapFrog Enterprises Inc. had the following quarterly net incomes during its 2009 fiscal year. (Source: Yahoo Finance) $$ \begin{array}{|c|c|} \hline \text { Quarter of Fiscal 2009 } & \text { Net Income (in millions) } \\\ \hline \text { First } & -27.1 \\ \hline \text { Second } & -12.2 \\ \hline \text { Third } & 7.2 \\ \hline \text { Fourth } & 29.4 \\ \hline \end{array} $$ What was the total net income for fiscal year \(2009 ?\)

Evaluate each expression. \(\frac{-20+(-4)^{2}(3)}{1-5}\)

Write each sentence as an equation or inequality. Use \(x\) to represent any unknown number. Thirteen minus three times a number is \(13 .\)

Evaluate each expression. \(\frac{(-4)^{2}-16}{4-12}\)

Write each sentence as an equation or inequality. Use \(x\) to represent any unknown number. Eight added to twice a number is 42 .