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hendricks_beginning_algebra_1e_ch1_3

Section 2.3 The Multiplication Property of Equality 121 SUMMARY OF KEY CONCEPTS 1. The multiplication property of equality enables us to multiply or divide both sides of an equation by the same nonzero number. 2. Most equations are going to require use of both the addition and multiplication properties of equality to solve them. The addition property of equality is used to eliminate terms from one side of the equation. The multiplication property of equality is used to make the coefficient of the variable one. 3. Word problems are solved by expressing the given relationships as a mathematical equation. 4. Consecutive integers are x, x + 1, x + 2, . . . . Consecutive even and odd integers are x, x + 2, x + 4, . . . . The equation used to solve these problems will be a result of direct translation. Refer to the key phrases learned in Chapter 1 and this chapter for assistance. GRAPHING CALCULATOR SKILLS The calculator should only be used to check that an equation was solved correctly at this point. Example: Verify that x=- 2 5 is a solution of 5x - 3 - 2x = 8x - 1. Method 1: Evaluate each side of the equation at the proposed solution. If each side produces the same number, then the solution is correct. 5a- 2 5 b - 3 - 2a- 2 5 b = 8a- 2 5 b - 1 Since each side of the equation produces the same result when evaluated at x=- 2 5 , the solution is correct. Method 2: Store the value of x into the calculator. Enter the equation and press enter. If a 1 is displayed, the statement is true for the stored value of x. If a 0 is displayed, the statement is false for the stored value of x. ( ) 2 4 5 T u n ENTER T 5 T u n 2 3 2 2 T u n 2nd ENTER MATH 1 8 T u n 2 1 Since 1 is displayed, the solution is correct. ? Write About It! Use complete sentences in your answers to the following exercises. 1. Explain the multiplication property of equality. 2. Give an example of an equation that requires use of the addition property of equality to solve it, but not the multiplication property of equality. Explain your answer. 3. Give an example of an equation that requires use of the multiplication property of equality to solve it, but not the addition property of equality. Explain your answer. 4. Give an example of an equation that requires use of both the additional and multiplication properties of equality to solve it. Explain your answer. Determine if each statement is true or false. If a statement is false, explain why. 5. The equation, -p = 5, is solved for p. 6. To solve the equation -3x = 6, add three to both sides. 7. The solution of 1 4 x = 3 is x = 12. �� ���������������� �������� EXERCISE SET


hendricks_beginning_algebra_1e_ch1_3
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