96 Chapter 2 Linear Equations and Inequalities in One Variable Solution 4b. What is unknown? The earnings of each celebrity are unknown. Let j represent James Cameron’s earnings. Winfrey’s earnings are $105 million more than Cameron’s, so j + 105 represents Winfrey’s earnings. What is known? They earned a combined total of $525 million. The phrase “of ” represents the equals sign. “They earned a combined total” represents the left side of the equation. “525” represents the right side of the equation. They earned a combined total of 525 j + j + 105 = 525 So, the equation used to solve this problem is j + j + 105 = 525. Student Check 4 For each problem, define a variable and write an equation that can be used to solve the problem. a. One angle is 20° less than another angle. The angles are supplementary. Find the measure of each angle. b. The total number of U.S. deaths from World War I and World War II was approximately 522 thousand. The number of deaths from World War I was 288 thousand less than the number of deaths from World War II. How many deaths occurred in each world war? (Source: http://www.fas.org/sgp/crs/natsec/ RL32492.pdf ) Troubleshooting Common Errors Some common errors associated with determining if a value is a solution of an equation and translating expressions are shown next. �� ������������������������ ������������������ A problem and an incorrect solution are given. Provide the correct solution and an explanation of the error. 5a. Is 4x - 2 - 6x + 4 an equation or expression? �������������������������������������� ���������������������������������������������������������������� 4x - 2 - 6x + 4 does not contain an equals sign, so this is an expression, not an equation. equatio 5b. Determine if x = -5 is a solution of 3 - 2(x + 4) = 5. �������������������������������������� ���������������������������������������������������������������� The error was made in evaluating the left side of the equation. After simplifying what is in parentheses, we should multiply before adding. 3 - 2(x + 4) = 5 3 - 2(-5 + 4) = 5 3 - 2(-1) = 5 3 + 2 = 5 5 = 5 Since x = -5 makes the equation true, it is a solution. Objective 5 ▶ Troubleshoot common errors. 4x - 2 - 6x + 4 is an equation. 3 - 2(x + 4) = 5 3 2(-5 + 4) = 5 - 2 3 - 3 2(-1) = 5 1( 1(-1) = 5 1 = 5 - ince this is a false statement = - on. Since statement, x 5 is not a solution.
hendricks_beginning_algebra_1e_ch1_3
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