167 Summary Exercises on Solving Equations Solve each equation for the specified variable. (Assume all denominators are nonzero.) 105. d = k2h, for h 106. x 2/3 + y2/3 = a2/3, for y 107. m3/4 + n3/4 = 1, for m 108. 1 R = 1 r1 + 1 r2 , for R 109. E e = R + r r , for e 110. a2 + b2 = c2, for b Relating Concepts For individual or collaborative investigation (Exercises 111–114) In this section we introduced methods of solving equations quadratic in form by substitution and solving equations involving radicals by raising each side of the equation to a power. Suppose we wish to solve x - 2x - 12 = 0. We can solve this equation using either of the two methods. Work Exercises 111–114 in order, to see how both methods apply. 111. Let u = 2x and solve the equation by substitution. 112. Solve the equation by isolating 2x on one side and then squaring. 113. Which one of the methods used in Exercises 111 and 112 do you prefer? Why? 114. Solve 3x - 22x - 8 = 0 using one of the two methods described. Summary Exercises on Solving Equations This section of miscellaneous equations provides practice in solving all the types introduced in this chapter so far. Solve each equation. 1. 4x - 3 = 2x + 3 2. 5 - 16x + 32 = 212 - 2x2 3. x1x + 62 = 9 4. x2 = 8x - 12 5. 2x + 2 + 5 = 2x + 15 6. 5 x + 3 - 6 x - 2 = 3 x2 + x - 6 7. 3x + 4 3 - 2x x - 3 = x 8. x 2 + 4 3 x = x + 5 9. 5 - 2 x + 1 x2 = 0 10. 12x + 122 = 9 19. 114 - 2x22/3 = 4 20. -x-2 + 2x-1 = 1 21. x x - 2 = 2 x - 2 + 2 22. a2 + b2 = c2, for a 11. x-2/5 - 2x-1/5 - 15 = 0 12. 2x + 2 + 1 = 22x + 6 13. x4 - 3x2 - 4 = 0 14. 1.2x + 0.3 = 0.7x - 0.9 15. 23 2x + 1 = 23 9 16. 3x2 - 2x = -1 17. 332x - 16 - 2x2 + 14 = 5x 18. 2x + 1 = 211 - 1x
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