Section 1.1 Linear Equations in One Variable 53 Answers 12. Contradiction; 5 6 13. Identity; 14. Conditional equation; 516 5x 0 x is a real number6 Solution: a. Clear parentheses. Combine like terms. Contradiction 5 6 3 3x 1x 12 4 2 3 3x x 14 2 3 314 2 3 2 This equation is a contradiction.The solution set is . b. Clear parentheses and combine like terms. Identity 5c 0 c is a real number6 513 c2 2 2c 3c 17 15 5c 2 5c 17 5c 17 5c 17 0 0 This equation is an identity.The solution set is . c. 4x 3 17 4x 20 x 5 This equation is a conditional equation.The solution set is 556. Skill Practice Identify each equation as a conditional equation, an identity, or a contradiction.Then give the solution set. 12. 21 5x 12 2x 12x 6 13. 213x 12 61x 12 8 14. 4x 1 x 6x 2 TIP: Interval notation can also be used to express the set of real numbers, 1 . , 2 Section 1.1 Practice Exercises Study Skills Exercise Some instructors allow the use of calculators. Does your instructor allow the use of a calculator? If so, what kind? Will you be allowed to use a calculator on tests or just for occasional calculator problems in the text? Helpful Hint: If you are not permitted to use a calculator on tests, you should do your homework in the same way, without the calculator. Vocabulary and Key Concepts 1. a. An is a statement that indicates that two quantities are equal. b. A to an equation is a value of the variable that makes the equation a true statement. c. An equation that can be written in the form is called a equation in one variable. ax b c 1a 02 d. A linear equation is also called a -degree equation because the degree on the variable is 1. e. The set of all solutions to an equation is called the . f. Two equations are equivalent if they have the same set. g. A equation is true for some values of the variable, but false for other values.
miller_intermediate_algebra_4e_ch1_3
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