Section 2.1 Addition, Subtraction, Multiplication, and Division Properties of Equality 129 Section 2.1 Practice Exercises Study Skills Exercise After getting a test back, it is a good idea to correct the test so that you do not make the same errors again. One recommended approach is to use a clean sheet of paper, and divide the paper down the middle vertically as shown. For each problem that you missed on the test, rework the problem correctly on the left-hand side of the paper. Then give a written explanation on the right-hand side of the paper. To reinforce the correct procedure, do four more problems of that type. For additional exercises, see Classroom Activities 2.1A–2.1D in the Student’s Resource Manual at www.mhhe.com/moh. Take the time this week to make corrections from your last test. Vocabulary and Key Concepts 1. a. An is a statement that indicates that two expressions are equal. Perform the correct math here. 2 4(5) 2 20 22 Explain the process here. Do multiplication before addition. 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 Concept 1: Definition of a Linear Equation in One Variable For Exercises 2–6, identify the following as either an expression or an equation. 2. 3. 4. 2 8x 10 x 4 5x 8x 2 7 Expression Expression Equation 9 2x 4 3x2 x 3 5. 6. Equation Equation 7. Explain how to determine if a number is a solution to an equation. Substitute the value into the equation and determine if the right-hand side is equal to the left-hand side. 8. Explain why the equations 6x 12 and x 2 are equivalent equations. They are equivalent equations because their solutions are the same. The solution is 2 in both cases. For Exercises 9–14, determine whether the given number is a solution to the equation. (See Example 1.) 9. No 10. No 11. Yes x 1 5; 4 x 2 1; 1 5x 10; 2 3x 21; 7 3x 9 3; 2 2x 1 3; 1 12. Yes 13. Yes 14. Yes Concept 2: Addition and Subtraction Properties of Equality For Exercises 15–34, solve the equations using the addition or subtraction property of equality. Be sure to check your answers. (See Examples 2 and 3.) 15. x 6 5 1 16. x 2 10 12 17. q 14 6 20 18. w 3 5 8 19. 2 m 15 17 20. 6 n 10 16 21. 23 y 7 16 22. 9 21 b 12 23. 4 c 4 0 24. 13 b 13 0 25. 4.1 2.8 a 1.3 26. 5.1 2.5 y 7.6 2 3 7 3 5 2 1 2 2 3 1 2 27. 5 z 28. 7 p 29. x 2 30. x 3 31. 6.02 c 8.15 32. p 0.035 1.12 33. 3.245 t 0.0225 34. 1.004 k 3.0589 Writing Translating Expression Geometry Scientific Calculator Video equation linear solution 23 3 11 2 2.13 1.155 3.2675 4.0629
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