Chapter 1

Evaluate \(3 x+4(y+6)\) when \(x\) is 1 less than the quotient of \(y\) and \(3,\) and \(y=15\)

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

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. Exercises \(79-80\) involve these deficits. (GRAPH CANT 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

In Exercises \(77-96,\) simplify each algebraic expression. $$-4\left(-\frac{3}{4} y\right)$$

Evaluate each algebraic expression for the given value of the variable. $$\frac{6 y-4 y^{2}}{y^{2}-15} ; y=5$$

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

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

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. $$\frac{3}{4}+\frac{3}{20}$$

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. Exercises \(79-80\) involve these deficits. (GRAPH CANT COPY) a. In \(2006,\) the government collected \(\$ 2407\) billion and spent \(\$ 2655\) billion. Find \(2407+(-2655)\) and determine the deficit, in billions of dollars, for 2006 b. In \(2007,\) the government collected \(\$ 2568\) billion and spent \(\$ 2730\) 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

Evaluate each algebraic expression for the given value of the variable. $$\frac{3 y-2 y^{2}}{y(y-2)} ; y=5$$

In Exercises \(77-96,\) simplify each algebraic expression. $$-5\left(-\frac{3}{5} y\right)$$

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

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

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. $$\frac{2}{5}+\frac{2}{15}$$

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

Simplify each algebraic expression by removing parentheses and brackets. $$3[5(x-2)+1]$$

In Exercises \(77-96,\) simplify each algebraic expression. $$8 x+x$$

What are equivalent algebraic expressions?

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

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. $$\frac{3}{8}+\frac{5}{12}$$

What are additive inverses?

Simplify each algebraic expression by removing parentheses and brackets. $$4[6(x-3)+1]$$

In Exercises \(77-96,\) simplify each algebraic expression. $$12 x+x$$

State a commutative property and give an example.

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

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. $$\frac{3}{10}+\frac{2}{15}$$

Describe how the inverse property of addition $$a+(-a)=0$$ can be shown on a number line.

Simplify each algebraic expression by removing parentheses and brackets. $$3[6-(y+1)]$$

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

State an associative property and give an example.

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

Simplify each algebraic expression. \(-5 x-10 y-3 x+13 y\)

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

Without using a number line, describe how to add two numbers with the same sign. Give an example.

Simplify each algebraic expression by removing parentheses and brackets. $$5[2-(y+3)]$$

In Exercises \(77-96,\) simplify each algebraic expression. $$-6 x+x$$

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

Simplify each algebraic expression. \(-6 x-9 y-4 x+15 y\)

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{17}{18}-\frac{4}{9}$$

Without using a number line, describe how to add two numbers with different signs. Give an example.

Simplify each algebraic expression by removing parentheses and brackets. $$7-4[3-(4 y-5)]$$

In Exercises \(77-96,\) simplify each algebraic expression. $$6 b-7 b$$

Explain how to add like terms. Give an example.

Insert either \(<,>,\) or \(=\) in the shaded area to make a true statement. $$\frac{8}{13} \div \frac{8}{13} \quad\square\quad|-1|$$

Find the value of each expression. $$-|-9-(-6)|-(-12)$$

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