Chapter 1

In Exercises \(29-72,\) use the order of operations to simplify each expression. $$\frac{\frac{7}{9}-3}{\frac{5}{6}} \div \frac{3}{2}+\frac{3}{4}$$

Perform the indicated division or state that the expression is undefined. $$-\frac{14}{9} \div \frac{7}{8}$$

Write each English phrase as an algebraic expression. Then simplify the expression. Let \(x\) represent the number. six times the product of 4 and a number

Solve by writing a sum of signed numbers and adding. The greatest temperature variation recorded in a day is 100 degrees in Browning, Montana, on January \(23,1916\). The low temperature was \(-56^{\circ} \mathrm{F}\). What was the high temperature?

Write each sentence as an equation. Let the variable \(x\) represent the number. The product of 4 and a number increased by 5 is 33

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{5}{8}+\frac{5}{8}$$

Identify the terms in each algebraic expression. $$8 a-7 a b-13$$

Find each absolute value. $$|3|$$

In Exercises \(29-72,\) use the order of operations to simplify each expression. $$\frac{\frac{17}{25}}{\frac{3}{5}-4} \div \frac{1}{5}+\frac{1}{2}$$

Perform the indicated division or state that the expression is undefined. $$-\frac{5}{16} \div \frac{25}{8}$$

Write each English phrase as an algebraic expression. Then simplify the expression. Let \(x\) represent the number. nine times the product of 3 and a number

Solve by writing a sum of signed numbers and adding. In Spearfish, South Dakota, on January \(22,1943,\) the temperature rose 49 degrees in two minutes. If the initial temperature was \(-4^{\circ} \mathrm{F},\) what was the temperature two minutes later?

Write each sentence as an equation. Let the variable \(x\) represent the number. The product of 6 and a number increased by 3 is 33

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{3}{8}+\frac{3}{8}$$

Simplify each algebraic expression. $$3 x-9 x$$

Find each absolute value. $$|-7|$$

In Exercises \(73-80,\) evaluate each algebraic expression for the given value of the variable. $$x^{2}+5 x ; x=3$$

Perform the indicated division or state that the expression is undefined. $$\frac{1}{3} \div\left(-\frac{1}{3}\right)$$

Write each English phrase as an algebraic expression. Then simplify the expression. Let \(x\) represent the number. six times the sum of 4 and a number

Solve by writing a sum of signed numbers and adding. The Dead Sea is the lowest elevation on Earth, 1312 feet below sea level. What is the elevation of a person standing 712 feet above the Dead Sea?

Write each sentence as an equation. Let the variable \(x\) represent the number. Five times a number is equal to 24 decreased by the number.

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{7}{12}-\frac{5}{12}$$

Simplify each algebraic expression. $$2 x-10 x$$

Find each absolute value. $$|-9|$$

In Exercises \(73-80,\) evaluate each algebraic expression for the given value of the variable. $$x^{2}-2 x ; x=6$$

Perform the indicated division or state that the expression is undefined. $$\frac{1}{5} \div\left(-\frac{1}{5}\right)$$

Write each English phrase as an algebraic expression. Then simplify the expression. Let \(x\) represent the number. nine times the sum of 3 and a number

Solve by writing a sum of signed numbers and adding. Lake Assal in Africa is 512 feet below sea level. What is the elevation of a person standing 642 feet above Lake Assal?

Write each sentence as an equation. Let the variable \(x\) represent the number. Four times a number is equal to 25 decreased by the number.

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{13}{18}-\frac{5}{18}$$

Simplify each algebraic expression. $$4+7 y-17 y$$

In Exercises \(73-80,\) evaluate each algebraic expression for the given value of the variable. $$3 x^{2}-8 x ; x=-2$$

Find each absolute value. $$\left|\frac{5}{6}\right|$$

Perform the indicated division or state that the expression is undefined. $$6 \div\left(-\frac{2}{5}\right)$$

Write each English phrase as an algebraic expression. Then simplify the expression. Let \(x\) represent the number. eight increased by the product of 5 and one less than a number

Write each sentence as an equation. Let the variable \(x\) represent the number. Evaluate \(\frac{x-y}{4}\) when \(x\) is 2 more than 7 times \(y\) and \(y=5\)

Solve by writing a sum of signed numbers and adding. The temperature at 8: 00 A.M. was \(-7^{\circ} \mathrm{F}\). By noon it had risen \(15^{\circ} \mathrm{F},\) but by \(4: 00 \mathrm{P.M.}\) it had fallen \(5^{\circ} \mathrm{F}\). What was the temperature at 4: 00 P.M.?

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{16}{7}-\frac{2}{7}$$

Simplify each algebraic expression. $$5+9 y-29 y$$

Find each absolute value. $$\left|\frac{4}{5}\right|$$

In Exercises \(73-80,\) evaluate each algebraic expression for the given value of the variable. $$4 x^{2}-2 x ; x=-3$$

Perform the indicated division or state that the expression is undefined. $$8 \div\left(-\frac{2}{9}\right)$$

Write each English phrase as an algebraic expression. Then simplify the expression. Let \(x\) represent the number. nine increased by the product of 3 and 2 less than a number

Write each sentence as an equation. Let the variable \(x\) represent the number. Evaluate \(\frac{x-y}{3}\) when \(x\) is 2 more than 5 times \(y\) and \(y=4 .\)

Solve by writing a sum of signed numbers and adding. On three successive plays, a football team lost 15 yards, gained 13 yards, and then lost 4 yards. What was the team's total gain or loss for the three plays?

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{17}{5}-\frac{2}{5}$$

Simplify each algebraic expression. $$2 a+5-9 a$$

In Exercises \(73-80,\) evaluate each algebraic expression for the given value of the variable. $$-x^{2}-10 x ; x=-1$$

Find each absolute value. $$|-\sqrt{11}|$$

Simplify each algebraic expression. $$-5(2 x)$$