Chapter 1

Solve by writing a sum of signed numbers and adding. \(\begin{array}{lllllllll}\text { A } & \text { football } & \text { team } & \text { started } & \text { with } & \text { the } & \text { football } & \text { at } & \text { the }\end{array}\) 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?

Write each sentence as an equation. Let the variable \(x\) represent the number. 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. $$\frac{1}{2}+\frac{1}{5}$$

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

In Exercises \(73-80,\) 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. $$-9(3 x)$$

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?

Write each sentence as an equation. Let the variable \(x\) represent the number. Evaluate \(3 x+4(y+6)\) when \(x\) is 1 less than the quoticnt of \(y\) and \(3,\) and \(y=15\)

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

Simplify each algebraic expression. $$4-6 b-8-3 b$$

In Exercises \(73-80,\) evaluate each algebraic expression for the given value of the variable. $$\frac{6 y-4 y^{2}}{y^{2}-15} ; y=5$$

Simplify each algebraic expression. $$-4\left(-\frac{3}{4} y\right)$$

What is a term? Provide an example with your description.

The bar graph shows that in 2000 and 2001 , the U.S. government collected more in taxes than it spent, so there was a budget surplus for each of these years. By contrast, in 2002 through \(2009,\) the government spent more than it collected, resulting in budget deficits. (GRAPH CAN NOT COPY) a. In \(2008,\) the government collected \(\$ 2521\) billion and spent \(\$ 2931\) billion. Find \(2521+(-2931)\) and determine the deficit, in billions of dollars, for 2008 . b. In \(2009,\) the government collected \(\$ 2700\) billion and spent \(\$ 3107\) billion. Find the deficit, in billions of dollars, for 2009 c. Use your answers from parts (a) and (b) to determine the combined deficit, in billions of dollars, for 2008 and 2009

Write each sentence as an equation. Let the variable \(x\) represent the number. a. Evaluate \(2(x+3 y)\) for \(x=4\) and \(y=1\) b. Is the number you obtained in part (a) a solution of $$ 5 z-30=40 ? $$

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{3}{4}+\frac{3}{20}$$

Simplify each algebraic expression. $$5-7 b-13-4 b$$

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

Simplify each algebraic expression. $$-5\left(-\frac{3}{5} y\right)$$

What are like terms? Provide an example with your description.

The bar graph shows that in 2000 and 2001 , the U.S. government collected more in taxes than it spent, so there was a budget surplus for each of these years. By contrast, in 2002 through \(2009,\) the government spent more than it collected, resulting in budget deficits. (GRAPH CAN NOT COPY) a. In \(2006,\) the government collected 2407 dollar billion and spent 2655 dollar billion. Find \(2407+(-2655)\) and determine the deficit, in billions of dollars, for 2006 b. In \(2007,\) the government collected 2568 dollar billion and spent 2730 dollar billion. Find the deficit, in billions of dollars, for 2007 . c. Use your answers from part (a) and (b) to determine the combined deficit, in billions of dollars, for 2006 and 2007

Write each sentence as an equation. Let the variable \(x\) represent the number. a. Evaluate \(3(2 x+y)\) for \(x=1\) and \(y=5\) b. Is the number you obtained in part (a) a solution of \(4 z-30=54 ?\)

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{2}{5}+\frac{2}{15}$$

Simplify each algebraic expression. $$13-(-7 x)+4 x-(-11)$$

In Exercises \(81-88,\) simplify each algebraic expression by removing parentheses and brackets. $$3[5(x-2)+1]$$

Insert either \(<,>,\) or \(=\) in the shaded area to make a true statement. $$\left|\frac{3}{5}\right|\square|-0.6|$$

Simplify each algebraic expression. $$8 x+x$$

What are equivalent algebraic expressions?

Explain how to add two numbers with a number line. Provide an example with your explanation.

Write each sentence as an equation. Let the variable \(x\) represent the number. a. Evaluate \(6 x-2 y\) for \(x=3\) and \(y=6\) b. Is the number you obtained in part (a) a solution of $$ 7 w=45-2 w ? $$

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{3}{8}+\frac{5}{12}$$

Simplify each algebraic expression. $$15-(-3 x)+8 x-(-10)$$

In Exercises \(81-88,\) simplify each algebraic expression by removing parentheses and brackets. $$4[6(x-3)+1]$$

Simplify each algebraic expression. $$12 x+x$$

State a commutative property and give an example.

What are additive inverses?

Write each sentence as an equation. Let the variable \(x\) represent the number. a. Evaluate \(5 x-14 y\) for \(x=3\) and \(y=\frac{1}{2}\) b. Is the number you obtained in part (a) a solution of \(4 w=54-5 w ?\)

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{3}{10}+\frac{2}{15}$$

Simplify each algebraic expression. $$-5 x-10 y-3 x+13 y$$

Insert either \(<,>,\) or \(=\) in the shaded area to make a true statement. $$\frac{30}{40}-\frac{3}{4} \square \frac{14}{15} \cdot \frac{15}{14}$$

In Exercises \(81-88,\) simplify each algebraic expression by removing parentheses and brackets. $$3[6-(y+1)]$$

Simplify each algebraic expression. $$-5 x+x$$

State an associative property and give an example.

Describe how the inverse property of addition $$a+(-a)=0$$

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{11}{18}-\frac{2}{9}$$

Simplify each algebraic expression. $$-6 x-9 y-4 x+15 y$$

In Exercises \(81-88,\) simplify each algebraic expression by removing parentheses and brackets. $$5[2-(y+3)]$$

Simplify each algebraic expression. $$-6 x+x$$

State a form of the distributive property and give an example.