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Section 2.2 Introduction to Applications 65 121. Solve 3x - 2(x + 4) = x + 5. David’s work: 3x - 2(x + 4) = x + 5 3x - 2x - 8 = x + 5 x - 8 = x + 5 x = 13 122. Solve 8 + 5(x - 1) = 3(2x + 1) - x. Amber’s work: 8 + 5(x - 1) = 3(2x + 1) - x 8 + 5x - 5 = 6x + 3 - x 5x + 3 = 5x + 3 0 = 0 So, the solution set is {0}. Calculate It! Use a graphing calculator to determine if -3, 1 2 , or 0 is a solution of the linear equation. 123. 6(1 - 3x) - 4x = 10(4 - x) 124. 3(20 - x) - 5x = 12(1 - 2x) 125. 10x - 9 5 =- 9 5 126. 9x - 8 3 =- 8 3 Think About It! 127. What value of c is required for -2 to be a solution of 4x + 3 = c? 128. What value of c is required for 1 2 to be a solution of -6x + 9 = c? 129. What value of b is required for -4 to be a solution of 3x + b = 10? 130. What value of b is required for 2 3 to be a solution of -6x + b = 1? 131. Complete the equation 3x - 2 = so that its solution set is . 132. Complete the equation -2x + 6 = so that its solution set is . 133. Complete the equation 8x + 3 = so that its solution set is . 134. Complete the equation 7x - 5 = so that its solution set is . SECTION 2.2 Introduction to Applications Iron Man 2 ranks tenth in the list of all-time opening weeks at the box office. It earned approximately $36.1 million more than Iron Man in its opening week. Together, they earned $282.3 million in their opening weeks. How much did Iron Man and Iron Man 2 each earn in their opening week? (Source: http://boxofficemojo.com/) To solve this problem, we need to know how to translate the given information into an equation. We will then use the process from Section 2.1 to solve the equation. Translating Statements into Linear Equations In Chapter 1, we discussed how to translate phrases into mathematical expressions. We can now combine this information with the properties that we learned in Section 2.1 to solve applications that can be translated into linear equations. Throughout this textbook, we will encounter applications that relate the mathematics that we are learning to real-life situations. Often the most difficult part of solving application problems is setting up the equation. So, some guidelines are provided. Procedure: Setting up Equations for Application Problems Step 1: Read the problem carefully and determine the unknown and assign a variable to it. Other unknowns in the problem should be represented in terms of the same variable initially chosen. Step 2: Determine what is given. Use this information as well as your knowledge of translating phrases into mathematical expressions to write the equation. Step 3: Solve the equation. Step 4: Check the proposed solution and state the result. ▶ OBJECTIVES As a result of completing this section, you will be able to 1. Translate applications into linear equations and solve. 2. Troubleshoot common errors. Objective 1 ▶ Translate applications into linear equations and solve.


hendricks_intermediate_algebra_1e_ch1_3
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