Exercises1.3 Section 1.3Solving Equationswith Variables on Both Sides 23Vocabulary and Core Concept CheckVocabularyand Core ConceptCheckIn Exercises 3–16, solve the equation. Check your solution.
(See Examples 1 and 2.)3.15 2x 3x 4. 26 4s 9s5.5p 9 2p + 12 6. 8g + 10 35 + 3g 7.5t + 16 6 5t 8. 3r + 10 15r 8 9. 7 + 3x 12x 3x + 1 10. w 2 + 2w 6 + 5w 11. 10(g + 5) 2(g + 9) 12. 9(t 2) 4(t 15) 13. 2 — 3 (3x + 9) 2(2x + 6) 14. 2(2t + 4) 3 — 4 (24 8t) 15. 10(2y + 2) y 2(8y 8) 16. 2(4x + 2) 4x 12(x 1) 17. MODELING WITH MATHEMATICS You and your friend drive toward each other. The equation 50h 190 45h represents the number h of hours until you and your friend meet. When will you meet? 18. MODELING WITH MATHEMATICS The equation 1.5r + 15 2.25r represents the number r of movies you must rent to spend the same amount at each movie store. How many movies must you rent to spend the same amount at each movie store? VIDEOCITYHIPMBEERSHMEMMMMMembership Fee: $15Membership Fee: FreeIn Exercises 19–24, solve the equation. Determine whether the equation has one solution, no solution, or innitely many solutions.
(See Example 3.)
19. 3t + 4 12 + 3t 20. 6d + 8 14 + 3d 21. 2(h + 1) 5h 7 22. 12y + 6 6(2y + 1) 23. 3(4g + 6) 2(6g + 9) 24. 5(1 + 2m) 1 — 2 (8 + 20m)ERROR ANALYSIS In Exercises 25 and 26, describe and correct the error in solving the equation. 25. 5c − 6 = 4 − 3c 2c − 6 = 4 2c = 10 c = 5
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26. 6(2y 6) = 4(9 3y)12y 36 = 36 12y12y = 12y0 = 0The equation has no solution.✗
27. MODELING WITH MATHEMATICS Write and solve an equation to nd the month when you would pay the same total amount for each Internet service.InstallationfeePrice per monthCompany A$60.00$42.95Company B$25.00$49.95Monitoring Progress and Modeling with MathematicsMonitoring Progress and Modeling with Mathematics 1. VOCABULARY Is the equation 2(4 x) 2x + 8 an identity? Explain your reasoning. 2. WRITING Describe the steps in solving the linear equation 3(3x 8) 4x + 6.Dynamic Solutionsavailable at BigIdeasMath.com
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