108 Chapter 2 Linear Equations and Inequalities in One Variable Troubleshooting Common Errors Some common errors associated with the addition property of equality are shown next. �� ������������������������ ������������������ A problem and an incorrect solution are given. Provide the correct solution and an explanation of the error. 5a. Solve 4 - x = 6. �������������������������������������� ���������������������������������������������������������������� The first step is correct in that we should subtract 4 from both sides. The resulting equation is incorrect. It should be 4 - x = 6 4 - x - 4 = 6 - 4 -x = 2 4 This tells us that the opposite of x is 2. Therefore, x must be the opposite of 2, which is -2. The solution set is {-2}. 4 = 2 T h l i i {2} The equation -x = 2 could also be solved by adding x to both sides and subtracting 2 from each side. -x = 2 -x + x = 2 + x 0 = x + 2 0 - 2 = x + 2 - 2 -2 = x 5b. Solve 3(x - 2) + 4 = 2x - 5. �������������������������������������� ���������������������������������������������������������������� Three was not distributed to the second term in the parentheses. 3(x - 2) + 4 = 2x - 5 3x - 6 + 4 = 2x - 5 3x - 2 = 2x - 5 3x - 2 - 2x = 2x - 5 - 2x x - 2 = -5 x - 2 + 2 = -5 + 2 x = -3 The solution set is {-3}. Objective 5 ▶ Troubleshoot common errors. 4 - x = 6 4 - x - = 6 - 4 x The solution set is 2}. 3(x - 2) + 4 4 = 2x 2x - 5 3x - 2 2 + 4 = 2x - 5 3x + 2 = 2x - 5 3x x + 2 - 2x = 2x - 5 - 2x x + 2 = - 5 x + 2 - 2 = -5 5 - 2 x = -7 The solution olution set is {-{ 7}. ANSWERS TO STUDENT CHECKS Student Check 1 a. linear equation b. linear equation c. not linear Student Check 2 a. {3} b. {-19} c. {2} d. {1.6} Student Check 3 a. {-5} b. {-3} c. {5} d. {18} e. {-14} Student Check 4 a. The number is -10. b. The student fees are $475. SUMMARY OF KEY CONCEPTS 1. A linear equation is an equation that can be written in the form ax + b = c, where a, b, and c are real numbers and a ≠ 0. The largest exponent of the variable term is one. 2. The addition property of equality enables us to add or subtract the same number from both sides of an equation. The key is to isolate the variable to one side of the equation. 3. To solve an equation, first simplify each side of the equation as much as possible. Then get variables on one side of the equation and constants on the other using the addition property of equality. 4. The key to solving applications is in setting up the equation that represents the given situation. Review Section 2.1 to assist you with this process.
hendricks_beginning_algebra_1e_ch1_3
To see the actual publication please follow the link above