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Example text

105. Describe the roster method for representing a set. 5x + 5, 106. What are the natural numbers? 107. What are the whole numbers? 108. What are the integers? where G represents the number of new college programs in green studies x years after 2005. Use this formula to solve ­Exercises 93–94. 109. Describe the rational numbers. 93. According to the formula, how many new college programs in green studies were created in 2009? Round to the nearest whole number. Does this rounded value underestimate or overestimate the actual number shown by the bar graph?

The Distributive Property Let a, b, and c represent real numbers, variables, or algebraic expressions. a(b+c)=ab+ac Multiplication distributes over addition. 24 Ch a p t e r 1 Algebra, Mathematical Models, and Problem Solving Great Question! E xample 11 What’s the most important thing I should keep in mind when using the distributive property? When using a distributive property to remove parentheses, be sure to multiply each term inside the parentheses by the factor outside. Incorrect 5(3y + 7) = 5 # 3y + 7 Using the Distributive Property Use the distributive property to write an equivalent expression: -2(3x + 5).

A + (-a) = 0 and (-a) + a = 0 The symbol ;-< is used to name the opposite, or additive inverse, of a. When a is a negative number, -a, its opposite, is positive. For example, if a is -4, its opposite is 4. Thus, –(–4) =4. The opposite of −4 is 4. In general, if a is any real number, -(-a) = a. Example 3 Finding Opposites Find -x if a. x = -6 b. x = 1 . 2 18 Ch a p t e r 1 Algebra, Mathematical Models, and Problem Solving Solution a. If x = -6, then -x = -(-6) = 6. The opposite of -6 is 6. 1 1 1 1 b.