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hendricks_beginning_algebra_1e_ch1_3

120 Chapter 2 Linear Equations and Inequalities in One Variable Troubleshooting Common Errors Some common errors associated with solving linear equations are shown next. It is very important to be able to distinguish when the addition property of equality applies and when the multiplication property of equality applies. We use the addition property of equality to remove terms from one side of the equation. The multiplication property of equality is used to obtain a coefficient of one on the variable. �� ������������������������ ������������������ A problem and an incorrect solution are given. Provide the correct solution and an explanation of the error. 5a. Solve -2x = 30. �������������������������������������� ���������������������������������������������������������������� The expression -2x + 2 cannot be combined since they are not like terms. So, adding 2 to both sides will not isolate x. Note that -2 is the coefficient of x. So, we divide both sides by -2 to obtain a coefficient of 1 on the variable. -2x -2 = 30 -2 x=-15 he 32 The solution set is {-15}. 5b. Solve 2x + 8 = 4x + 10. �������������������������������������� ���������������������������������������������������������������� The first step of subtracting 4x from both sides was applied incorrectly on the left side of the equation. We should subtract 4x at the end of the terms on the left, not insert it at the beginning. 2x + 8 = 4x + 10 2x + 8 - 4x = 4x - 4x + 10 -2x + 8 = 10 -2x + 8 - 8 = 10 - 8 -2x = 2 2x -= -2 2 -2 x=-1 The solution set is {-1}. Objective 5 ▶ Troubleshoot common errors. -2x = 30 -2x + 2 = 30 + 2 x = 32 The solution set is {32}. 2x + 8 = 4x + 10 4x - 2x + 8 = 4x - 4x + 10 2x + 8 = 10 2x + 8 - 8 = 10 - 8 2x = 2 x = 1 The solution set is {1}. 2 he 1} ANSWERS TO STUDENT CHECKS Student Check 1 a. {-7} b. {60} c. {8} d. {-16} e. {-45} Student Check 2 a. {3} b. e 7 11 f c. e 1 2 f d. e- 20 3 f Student Check 3 a. The number is -3. b. It takes 600 nickels to make $30. c. The car can be driven for 180 miles for a cost of $50. Student Check 4 a. The integers are -69 and -68. b. The integers are 14, 16, and 18.


hendricks_beginning_algebra_1e_ch1_3
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