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hendricks_intermediate_algebra_1e_ch1_3

62 Chapter 2 Linear Equations and Inequalities in One Variable ANSWERS TO STUDENT CHECKS Student Check 1 a. linear; yes b. linear; no c. not linear Student Check 2 a. 5-4.86 b. 5-126 Student Check 3 a. 5-106 b. 536 Student Check 4 a. 5-36 b. 516 c. e 1 5 f d. 5126 Student Check 5 Student Check 6 SUMMARY OF KEY CONCEPTS 1. A linear equation is an equation in which the exponent of the variable is 1. The standard form of the equation is ax + b = c. 2. The addition property of equality enables us to add the same number to each side of an equation or subtract the same number from each side of an equation and obtain an equivalent equation. 3. The multiplication property of equality enables us to multiply or divide each side of an equation by a nonzero number and obtain an equivalent equation. 4. To solve a linear equation, we must isolate the variable on one side of the equation. Clear fractions, decimals, and any parentheses. Then isolate the variable on one side of the equation and the constant on the other by applying the addition property. Finally, divide each side by the coefficient of the variable by applying the multiplication property. 5. A linear equation with no solution is a contradiction. This type of equation results when each side of the equation has the same variable term but different constant terms. The variables are eliminated from the equation and the resulting statement is false. 6. A linear equation with infinitely many solutions is an identity. All real numbers satisfy the equation. This type of equation results when each side of the equation has the same variable term and the same constant term. The variables are eliminated from the equation and the resulting statement is true. GRAPHING CALCULATOR SKILLS The graphing calculator can be used to determine if a number is a solution of an equation. Example: Determine if -2 is a solution of -4x + 2 = 2x - 1. Method 1: Use the calculator to evaluate the left and right side of the equation. Since the left side, 10, does not equal the right side, -5, the value -2 is not a solution of the equation. Method 2: Enter the left side and right side of the equation in the equation editor and use the table to determine the value of the each side. Y= (–) 4 X,T,u,n + 2 ENTER 2 X,T,u,n ENTER 2 2nd GRAPH When x=-2, the values in the columns for Y1 and Y2 are not equal. This shows that -2 is not a solution.


hendricks_intermediate_algebra_1e_ch1_3
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