Chapter 1

Name the property used to go from step to step each time that "(why?)" occurs. $$\begin{aligned} 7 &+2(x+9) \\ &=7+(2 x+18) \text { (why?) } \\ &=7+(18+2 x) \text { (why?) } \\ &=(7+18)+2 x \text { (why?) } \\ &=25+2 x \\ &=2 x+25 \text { (why?) } \end{aligned}$$

Determine whether each inequality is true or false. $$-9 \geq-9$$

Simplify each series of additions and subtractions. $$-0.16-5.2-(-0.87)$$

Write each sentence as an equation. Let the variable \(x\) represent the number. The sum of twice a number and 6 is 16

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$6 \frac{3}{5} \div 1 \frac{1}{10}$$

Insert either \(<,>,\) or \(=\) in the shaded area to make a true statement. $$[(-8)+(-6)]+10\quad\square\quad-8+[9+(-2)]$$

Perform the indicated division or state that the expression is undefined. $$ -10 \div 0 $$

Use the order of operations to simplify each expression. $$30 \div \frac{5^{2}}{7-12}-(-9)$$

Name the property used to go from step to step each time that "(why?)" occurs. $$\begin{aligned} 5 &(x+4)+3 x \\ &=(5 x+20)+3 x \quad \text { (why?) } \\ &=(20+5 x)+3 x \quad \text { (why?) } \\ &=20+(5 x+3 x) \text { (why?) } \\ &=20+(5+3) x \quad \text { (why?) } \\ &=20+8 x \\ &=8 x+20 \quad \text { (why?) } \end{aligned}$$

Determine whether each inequality is true or false. $$-14 \leq-14$$

Simplify each series of additions and subtractions. $$-1.9-3-(-0.26)$$

Write each sentence as an equation. Let the variable \(x\) represent the number. The sum of twice a number and 9 is 29

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$1 \frac{3}{4} \div 2 \frac{5}{8}$$

Write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. the sum of 7 times a number and twice the number

In Exercises \(47-76\), perform the indicated division or state that the expression is undefined. $$\frac{-12.9}{3}$$

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

Determine whether each inequality is true or false. $$0 \geq-6$$

Simplify each series of additions and subtractions. $$-\frac{3}{4}-\frac{1}{4}-\left(-\frac{5}{8}\right)$$

Write each sentence as an equation. Let the variable \(x\) represent the number. Five less than 3 times a number gives 7

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{2}{11}+\frac{4}{11}$$

Write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. the sum of 8 times a number and twice the number

In Exercises \(47-76\), perform the indicated division or state that the expression is undefined. $$\frac{-21.6}{3}$$

Use the order of operations to simplify each expression. $$\frac{\frac{3}{5}-\frac{7}{10}}{\frac{1}{2}}$$

Determine whether each inequality is true or false. $$0 \geq-13$$

Simplify each series of additions and subtractions. $$-\frac{1}{2}-\frac{2}{3}-\left(-\frac{1}{3}\right)$$

Write each sentence as an equation. Let the variable \(x\) represent the number. . Three less than 4 times a number gives 29 .

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{5}{13}+\frac{2}{13}$$

Write each English phrase as an algebraic expression. Then simplify the expression. Let \(x\) represent the number. The quotient of \(-20\) and a number, increased by the quotient of 3 and the number

Use the order of operations to simplify each expression. $$-\frac{9}{4}\left(\frac{1}{2}\right)+\frac{3}{4} \div \frac{5}{6}$$

Determine whether each inequality is true or false. $$-17 \geq 6$$

Identify the terms in each algebraic expression. $$-3 x-8 y$$

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. $$\frac{7}{12}+\frac{1}{12}$$

Write each English phrase as an algebraic expression. Then simplify the expression. Let \(x\) represent the number. The quotient of \(-15\) and a number, increased by the quotient of 4 and the number

In Exercises \(47-76\), perform the indicated division or state that the expression is undefined. $$-\frac{1}{2} \div\left(-\frac{7}{9}\right)$$

Use the order of operations to simplify each expression. $$\left[-\frac{4}{7}-\left(-\frac{2}{5}\right)\right]\left[-\frac{3}{8}+\left(-\frac{1}{9}\right)\right]$$

Determine whether each inequality is true or false. $$-14 \geq 8$$

Identify the terms in each algebraic expression. $$-9 a-4 b$$

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. $$\frac{5}{16}+\frac{1}{16}$$

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?

In Exercises \(47-76,\) perform the indicated division or state that the expression is undefined. \(-\frac{14}{9} \div \frac{7}{8}\)

Use the order of operations to simplify each expression. $$\frac{\frac{7}{9}-3}{\frac{5}{6}} \div \frac{3}{2}+\frac{3}{4}$$

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

Find each absolute value. $$|6|$$

Identify the terms in each algebraic expression. $$12 x-5 x y-4$$

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. $$\frac{5}{8}+\frac{5}{8}$$

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?

In Exercises \(47-76\), perform the indicated division or state that the expression is undefined. $$-\frac{5}{16} \div \frac{25}{8}$$