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1-4 Solving Equations Vocabulary Review Circle the equations. 2(3x 1 7) 5 10 3x 1 14 3x 1 2y 5 6 4x 1 (y 1 5) Vocabulary Builder x22x inverse operations (noun) IN vurs ahp uh RAY shunz inverse operations Related Words: opposite, reverse Main Idea: Inverse operations undo each other. Use Your Vocabulary 1. Write each inverse operation. Add 7. Subtract 4. Divide by 5. Key Concepts Properties of Equality Assume a, b, and c represent real numbers. Property Definition Example Reflexive aa 55 Symmetric If a b, then b a. (4)(2) 8, so 8 (4)(2) If a b and b c, then a c. 6 (2)(3) and (2)(3) (3)(2), so 6 (3)(2) If a b, then you can replace a with b and vice versa. If a b and 9 a 15, then 9 b 15 Transitive Substitution Chapter 1 14 Multiply by 3. Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved. Example: Addition and subtraction are inverse operations. Draw a line from each example in Column A to the property that it illustrates in Column B. Column A Column B 2. a 5 4 and a 1 b 5 5, so 4 1 b 5 5 Reflexive Property 3. 2 1 (x 1 8) 5 2 1 (x 1 8) Symmetric Property 4. x 1 y 5 z and z 5 4, so x 1 y 5 4 Transitive Property 5. y 1 12 5 9, so 9 5 y 1 12 Substitution Property Key Concepts Properties of Equality, Continued Assume a, b, and c represent real numbers. Property Definition Example Addition If a b, then a c b c. If x 12, then x 3 12 3. Subtraction If a b, then a c b c. If x 12, then x 3 12 3. Multiplication If a b, then a ∙ c b ∙ c. If x 12, then x ∙ 3 12 ∙ 3. Division If a b, then a c b c (with c 0). If x 12, then x 3 12 3. Write the Property of Equality that justifies each statement. Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved. 6. If x 1 2 5 5, then x 1 2 2 2 5 5 2 2. Property of Equality 4x 7. If 4x 5 12, then 4 5 12 4. x Property of Equality x 8. If 220 5 5 then 220 ? 5 5 5 ? 5. Property of Equality 9. If y 2 3 5 212 then y 2 3 1 3 5 212 1 3. Property of Equality Problem 1 Solving a One-Step Equation Got It? What is the solution of 12b 5 18? 10. Circle the multiplicative inverse of 12. 1 12 212 1 212 1 11. Use the multiplicative inverse to solve the equation and check your solution. 15 Lesson 1-4 Problem 2 Solving a Multi-Step Equation Division Property of Equality Got It? What is the solution of 3(2x 2 1) 2 2(3x 1 4) 5 11x? Combine like terms. Simplify. 12. The equation has been solved below. Use one of the reasons in the box to justify each step. Distributive Property 3(2x 2 1) 2 2(3x 1 4) 5 11x 6x 2 3 2 6x 2 8 5 11x 211 5 11x 11x 211 11 5 11 21 5 x Problem 3 Using Properties of Equations to Solve Problems Got It? The carpet at the right has perimeter 320 feet. What are the dimensions x of the carpet? 5 length of the carpet. 14. Use the formula for perimeter of a rectangle, P 5 2w 1 2/. Write an equation for the perimeter of the carpet. 15. Solve for x. 16. The width of the carpet is Problem 4 ft, and the length of the carpet is ft. Equations With No Solutions and Identities Got It? Is the equation 7x 1 6 2 4x 5 12 1 3x 2 8 always, sometimes, or never true? 17. Combine like terms on each side of the equation. 1 6 5 3x 1 18. Now solve the equation. 19. The equation is always / sometimes / never true. Chapter 1 16 3x Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved. 13. Let x 5 the width of the carpet. Then Problem 5 Solving a Literal Equation Got It? The equation S 5 3F 2 24 relates shoe size S and length of a foot in inches F. What is F in terms of S? 20. What two operations will you undo? _______________________________________________________________________ 21. Now solve the equation for F. Lesson Check • Do you UNDERSTAND? Reasoning Suppose you solve an equation and find that your school needs 4.3 buses for a class trip. Explain how to interpret this solution. 22. Why does the solution 4.3 not make sense as a solution to this problem? Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved. _______________________________________________________________________ _______________________________________________________________________ 23. What is the minimum number of buses that are needed for the trip? Explain. _______________________________________________________________________ _______________________________________________________________________ Math Success Check off the vocabulary words that you understand. equation solution inverse operations Rate how well you can solve equations. Need to review 0 2 4 6 8 10 Now I get it! 17 Lesson 1-4