118 Chapter 2 Linear Equations and Inequalities b. Clear parentheses. Subtract 2b from both sides. 21b 42 2b 7 2b 8 2b 7 2b 2b 8 2b 2b 7 (Contradiction) 8 7 This is a contradiction. Solution set: { } c. Subtract 2x from both sides. Simplify. Subtract 7 from both sides. 5126. 3x 7 2x 5 3x 2x 7 2x 2x 5 x 7 5 x 7 7 5 7 x 12 1Conditional equation2 This is a conditional equation.The solution set is (The equation is true only on the condition that x 12.2 Skill Practice Solve the equation. Identify the equation as a conditional equation, a contradiction, or an identity. 8. 412t 12 1 8t 3 9. 3x 5 4x 1 x 10. 61v 22 2v 4 Answers 8. The set of real numbers; identity 9. { }; contradiction 10. {2}; conditional equation Section 2.2 Practice Exercises Study Skills Exercise Several strategies are given here about taking notes. Check the activities that you routinely do and discuss how the other suggestions may improve your learning. Read your notes after class and complete any abbreviations or incomplete sentences. Highlight important terms and definitions. Review your notes from the previous class. Bring pencils (more than one) and paper to class. Sit in class where you can clearly read the board and hear your instructor. Turn off your cell phone and keep it off your desk to avoid distraction. Vocabulary and Key Concepts 1. a. A equation is true for some values of the variable, but false for other values. b. An equation that has no solution is called a . c. The set containing no elements is called the set. d. An equation that has all real numbers as its solution set is called an . Review Exercises For Exercises 2–5, simplify each expression by clearing parentheses and combining like terms. 2. 3. 5z 2 7z 3z 10 4w 7w 2 w 4. 17p 92 13p 12 5. 8y 12y 32 19
miller_beginning_intermediate_algebra_4e_ch1_3
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