Chapter 1

Insert \(<,>,\) or \(=\) in the appropriate space to make each statement true. $$ \left|-\frac{5}{8}\right| \quad\left|\frac{5}{8}\right| $$

Decide whether the given number is a solution of the given equation. \(-x-6=-x-1 ;-10\)

Simplify each of the following. See Example 17. $$ -(-8.4) $$

Write each phrase as an algebraic expression and simplify if possible. Let \(x\) represent the unknown number. Six times the difference of a number and five

Find the quotient of \(-\frac{5}{12}\) and \(\frac{5}{12}\).

Insert \(<,>,\) or \(=\) in the appropriate space to make each statement true. $$ \left|\frac{2}{5}\right| \quad\left|-\frac{2}{5}\right| $$

Decide whether the given number is a solution of the given equation. \(-x-13=-15 ; 2\)

Write each phrase as an algebraic expression and simplify if possible. Let \(x\) represent the unknown number. Double a number minus the sum of the number and ten

Perform the indicated operation. \(-9-10\)

Insert \(<,>,\) or \(=\) in the appropriate space to make each statement true. $$ |-2| \quad|-2.7| $$

Decide whether the given number is a solution of the given equation. \(4=1-x ; 5\)

Simplify each of the following. See Example 17. $$ -(-7 m) $$

Write each phrase as an algebraic expression and simplify if possible. Let \(x\) represent the unknown number. Half a number minus the product of the number and eight

Perform the indicated operation. \(-8-11\)

Insert \(<,>,\) or \(=\) in the appropriate space to make each statement true. $$ |-5.01|-|-5| $$

Solve. The coldest temperature ever recorded on Earth was \(-129^{\circ} \mathrm{F}\) in Antarctica. The warmest temperature ever recorded was \(136^{\circ} \mathrm{F}\) in the Sahara Desert. How many degrees warmer is \(136^{\circ} \mathrm{F}\) than \(-129^{\circ} \mathrm{F}\) ? (Source: Questions Kids Ask, Grolier Limited, 1991 , and The World Almanac)

Simplify each of the following. See Example 17. $$ \left|-\frac{2}{3}\right| $$

Perform the indicated operation. \(-9(-10)\)

Insert \(<,>,\) or \(=\) in the appropriate space to make each statement true. $$ |0| \quad|-8| $$

Solve. The coldest temperature ever recorded in the United States was \(-80^{\circ} \mathrm{F}\) in Alaska. The warmest temperature ever recorded was \(134^{\circ} \mathrm{F}\) in California. How many degrees warmer is \(134^{\circ} \mathrm{F}\) than \(-80^{\circ} \mathrm{F} ?\) (Source: The World Almanac, 2005)

Decide whether the given number is a solution of the given equation. $$ 4=1-x ; 1 $$

Simplify each of the following. See Example 17. $$ -\left|-\frac{2}{3}\right| $$

Perform the indicated operation. \(-8(-11)\)

Insert \(<,>,\) or \(=\) in the appropriate space to make each statement true. $$ |-12| \quad \frac{-24}{2} $$

Solve. Mauna Kea in Hawaii has an elevation of 13,796 feet above sea level. The Mid- America Trench in the Pacific Ocean has an elevation of 21,857 feet below sea level. Find the difference in elevation between those two points. (Source: National Geographic Society and Defense Mapping Agency)

Decide whether the given number is a solution of the given equation. $$ \frac{1}{3} x=9 ; 27 $$

Evaluate \(x+y\) for the given replacement values. See Examples 20 and 21. $$ x=-20 \text { and } y=-50 $$

Perform the indicated operation. 7(-12)

Solve. A woman received a statement of her charge account at Old Navy. She spent \(\$ 93\) on purchases last month. She returned an \(\$ 18\) top because she didn't like the color. She also returned a \(\$ 26\) nightshirt because it was damaged. What does she actually owe on her account?

Decide whether the given number is a solution of the given equation. $$ \frac{2}{7} x=\frac{3}{14} ; 6 $$

Perform the indicated operation. 6(-15)

Write each phrase as an algebraic expression. Let \(x\) represent the unknown number. Fifteen more than a number

Write each algebraic expression described. Write an expression with 4 terms that simplifies to \(3 x-4\)

Perform the indicated operation. \(7+(-12)\)

Write each phrase as an algebraic expression. Let \(x\) represent the unknown number. A number increased by 9

Write each algebraic expression described. Write an expression of the form ________(________+__________)whose product is 6x + 24.

Perform the indicated operation. 6+(-15)

A commercial jetliner hits an air pocket and drops 250 feet. After climbing 120 feet, it drops another 178 feet. What is its overall vertical change?

Write each phrase as an algebraic expression. Let \(x\) represent the unknown number. Five subtracted from a number

Translate each phrase; then simplify. See Example 22. Find the sum of -6 and 25.

Evaluate each expression. \(\frac{-9(-3)}{-6}\)

In some card games, it is possible to have a negative score. Lavonne Schultz currently has a score of 15 points. She then loses 24 points. What is her new score?

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

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

The highest point in Africa is Mt. Kilimanjaro, Tanzania, at an elevation of 19,340 feet. The lowest point is Lake Assal, Djibouti, at 512 feet below sea level. How much higher is Mt. Kilimanjaro than Lake Assal? (Source: National Geographic Society)

Write each phrase as an algebraic expression. Let \(x\) represent the unknown number. The ratio of a number and 4

Translate each phrase; then simplify. See Example 22. Find the sum of \(-31,-9,\) and 30 .

Write each algebraic expression described. To convert from feet to inches, we multiply by 12 . For example, the number of inches in 2 feet is \(12 \cdot 2\) inches. If one board has a length of \((x+2)\) fee and a second board has a length of \((3 x-1)\) inches, express their total length in inches as an algebraic expression.

Evaluate each expression. \(-3(2-8)\)

The airport in Bishop, California, is at an elevation of 4101 feet above sea level. The nearby Furnace Creek Airport in Death Valley, California, is at an elevation of 226 feet below sea level. How much higher in elevation is the Bishop Airport than the Furnace Creek Airport? (Source: National Climatic Data Center)