40 Chapter 1Solving Linear EquationsExercises1.5 Dynamic Solutionsavailable at BigIdeasMath.comIn Exercises 3–12, solve the literal equation for y. (See Example 1.)3.y 3x 13 4. 2x + y 75.2y 18x 26 6. 20x + 5y 157.9x y 45 8. 6 3y 69. 4x 5 7 + 4y 10. 16x + 9 9y 2x11. 2 + 1 — 6 y 3x + 4 12. 11 1 — 2 y 3 + 6xIn Exercises 13–22, solve the literal equation for x. (See Example 2.)13. y 4x + 8x 14. m 10x x15. a 2x + 6xz 16. y 3bx 7x17. y 4x + rx + 6 18. z 8 + 6x px19. sx + tx r 20. a bx + cx + d21.12 5x 4kx y 22. x 9 + 2wx y23. MODELING WITH MATHEMATICS The total cost C (in dollars) to participate in a ski club is given by the literal equation C 85x + 60, where x is the number of ski trips you take.a. Solve the equation for x.b. How many ski trips do you take if you spend a total of $315? $485?24. MODELING WITH MATHEMATICS The penny size of a nail indicates the length of the nail. The penny size d is given by the literal equation d 4n 2, where n is the length (in inches) of the nail.a. Solve the equation for n.b. Use the equation from part (a) to nd the lengths of nails with the following penny sizes: 3, 6, and 10.ERROR ANALYSIS In Exercises 25 and 26, describe and correct the error in solving the equation for x.25. 12 − 2x = −2(y − x) −2x = −2(y − x) − 12 x = (y − x) 6
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26. 10 = ax − 3b10 = x(a − 3b) 10 — a − 3b = x
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In Exercises 27–30, solve the formula for the indicated variable. (See Examples 3 and 5.)27. Prot: P R C; Solve for C.28. Surface area of a cylinder: S 2πr2 + 2πrh; Solve for h.29. Area of a trapezoid: A 1 — 2 h(b1 + b2); Solve for b2.30. Average acceleration of an object: a v1 v0 — t ; Solve for v1.Monitoring Progress and Modeling with MathematicsMonitoring Progress and Modeling with Mathematics 1. VOCABULARY Is 9r + 16 π — 5 a literal equation? Explain. 2. DIFFERENT WORDS, SAME QUESTION Which is different? Find “both” answers. Solve 3x + 6y 24 for x. Solve 24 3x 6y for x. Solve 6y 24 3x for y in terms of x. Solve 24 6y 3x for x in terms of y.Vocabulary and Core Concept CheckVocabularyand Core ConceptCheckn