Chapter 1

In Exercises \(29-72,\) use the order of operations to simplify each expression. $$-3^{2}+2[20 \div(7-11)]$$

Simplify each algebraic expression. $$11(6 a+3 b)+4(12 a+5 b)$$

Write each sentence as an equation. Let the variable \(x\) represent the number. The difference between 40 and a number is \(10 .\)

Find each sum. $$-25+[-|18+(-26)|]$$

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

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

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

Perform the indicated division or state that the expression is undefined. $$-4 \div 0$$

In Exercises \(29-72,\) use the order of operations to simplify each expression. $$24 \div \frac{3^{2}}{8-5}-(-6)$$

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

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. $$6 \frac{3}{5} \div 1 \frac{1}{10}$$

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

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

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

In Exercises \(29-72,\) 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. $$\begin{array}{l} 5(x+4)+3 x \\ =(5 x+20)+3 x \text { (why?) } \\ =(20+5 x)+3 x \text { (why?) } \\ =20+(5 x+3 x) \text { (why?) } \\ =20+(5+3) x \text { (why?) } \\ =20+8 x \\ =8 x+20 \text { (why?) } \end{array}$$

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

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

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

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

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

Perform the indicated division or state that the expression is undefined. $$\frac{-12.9}{3}$$

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

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

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. $$\frac{2}{11}+\frac{4}{11}$$

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

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

Perform the indicated division or state that the expression is undefined. $$\frac{-21.6}{3}$$

In Exercises \(29-72,\) use the order of operations to simplify each expression. $$\frac{\frac{3}{5}-\frac{7}{10}}{\frac{1}{2}}$$

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

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. $$\frac{5}{13}+\frac{2}{13}$$

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

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

Perform the indicated division or state that the expression is undefined. $$-\frac{1}{2} \div\left(-\frac{3}{5}\right)$$

In Exercises \(29-72,\) use the order of operations to simplify each expression. $$-\frac{9}{4}\left(\frac{1}{2}\right)+\frac{3}{4} \div \frac{5}{6}$$

Write each English phrase as an algebraic expression. Then simplify the expression. Let \(x\) represent the number. the product of 3 and a number, which is then subtracted from the product of 12 and a number

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

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

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

In Exercises \(29-72,\) use the order of operations to simplify each expression. $$\left[-\frac{4}{7}-\left(-\frac{2}{5}\right)\right]\left[-\frac{3}{8}+\left(-\frac{1}{9}\right)\right]$$

Perform the indicated division or state that the expression is undefined. $$-\frac{1}{2} \div\left(-\frac{7}{9}\right)$$

Write each English phrase as an algebraic expression. Then simplify the expression. Let \(x\) represent the number. the product of 5 and a number, which is then subtracted from the product of 11 and a number

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

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

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