Chapter 1

Use the order of operations to simplify each expression. $$\frac{\frac{17}{25}}{\frac{3}{5}-4} \div \frac{1}{5}+\frac{1}{2}$$

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

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

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

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. $$\frac{3}{8}+\frac{3}{8}$$

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?

In Exercises \(47-76\), perform the indicated division or state that the expression is undefined. $$\frac{1}{3} \div\left(-\frac{1}{3}\right)$$

Evaluate each algebraic expression for the given value of the variable. $$x^{2}+5 x ; x=3$$

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

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

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

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. $$\frac{7}{12}-\frac{5}{12}$$

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?

In Exercises \(47-76\), perform the indicated division or state that the expression is undefined. $$\frac{1}{5} \div\left(-\frac{1}{5}\right)$$

Evaluate each algebraic expression for the given value of the variable. $$x^{2}-2 x ; x=6$$

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

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

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

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. $$\frac{13}{18}-\frac{5}{18}$$

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 \(4: 00 \mathrm{P} .\). \(\mathrm{M} .\) it had fallen \(5^{\circ} \mathrm{F}\). What was the temperature at 4: 00 P.M.?

In Exercises 47-76, perform the indicated division or state that the expression is undefined. $$ 6 \div\left(-\frac{2}{5}\right) $$

Evaluate each algebraic expression for the given value of the variable. $$3 x^{2}-8 x ; x=-2$$

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

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

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

Evaluate \(\frac{x-y}{4}\) when \(x\) is 2 more than 7 times \(y\) and \(y=5\)

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

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

Evaluate each algebraic expression for the given value of the variable. $$4 x^{2}-2 x ; x=-3$$

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

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

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

Evaluate \(\frac{x-y}{3}\) when \(x\) is 2 more than 5 times \(y\) and \(y=4\)

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

Solve by writing a sum of signed numbers and adding. A football team started with the football at the 27-yard line, advancing toward the center of the field (the 50-yard line). Four successive plays resulted in a 4 -yard gain, a 2 -yard loss, an 8 -yard gain, and a 12 -yard loss. What was the location of the football at the end of the fourth play?

In Exercises \(77-96,\) simplify each algebraic expression. $$-5(2 x)$$

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. $$2 a+5-9 a$$

Evaluate \(4 x+3(y+5)\) when \(x\) is 1 less than the quotient of \(y\) and 4 and \(y=12\)

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{1}{2}+\frac{1}{5}$$

Solve by writing a sum of signed numbers and adding. The water level of a reservoir is measured over a five-month period. At the beginning, the level is 20 feet. During this time, the level rose 3 feet, then fell 2 feet, then fell 1 foot, then fell 4 feet, and then rose 2 feet. What is the reservoir's water level at the end of the five months?

In Exercises \(77-96,\) simplify each algebraic expression. $$-9(3 x)$$

Evaluate each algebraic expression for the given value of the variable. $$-x^{2}-14 x ; x=-1$$

Find each absolute value. $$|-\sqrt{29}|$$

Simplify each algebraic expression. $$3 a+7-11 a$$