1. Problem: Simplify the expression for the cost of a dress after a 6% tax, given by $d + 0.06d$. 2. Formula: When adding like terms, add their coefficients. 3. Work: $$d + 0.06d = (1 + 0.06)d = 1.06d$$ 4. Explanation: We combined the terms by adding the coefficients 1 and 0.06 because both terms have the variable $d$. 5. Final answer: $1.06d$ 6. Problem: Simplify the expression for the cost of a tablet after a 20% discount, given by $t - 0.2t$. 7. Work: $$t - 0.2t = (1 - 0.2)t = 0.8t$$ 8. Explanation: We subtracted the coefficients because the second term is being subtracted. 9. Final answer: $0.8t$ 10. Problem: Simplify $4a + 7c - 2 - 5a + 2c$. 11. Group like terms: $$(4a - 5a) + (7c + 2c) - 2$$ 12. Simplify: $$-1a + 9c - 2$$ 13. Final answer: $-1a + 9c - 2$ 14. Problem: Simplify $8 - 7x + 2y - 3x + 2y + 3$. 15. Group like terms: $$(8 + 3) + (-7x - 3x) + (2y + 2y)$$ 16. Simplify: $$11 - 10x + 4y$$ 17. Final answer: $11 - 10x + 4y$ 18. Problem: Simplify $12p + 3q - 5 - 5q - 8p$. 19. Group like terms: $$(12p - 8p) + (3q - 5q) - 5$$ 20. Simplify: $$4p - 2q - 5$$ 21. Final answer: $4p - 2q - 5$ 22. Problem: Simplify $6z - 2y - 8z + 5y - 4 + z$. 23. Group like terms: $$(6z - 8z + z) + (-2y + 5y) - 4$$ 24. Simplify: $$(6 - 8 + 1)z + ( -2 + 5)y - 4 = -1z + 3y - 4$$ 25. Final answer: $-1z + 3y - 4$ 26. Problem: Simplify $\frac{1}{5}x - \frac{4}{7} + \frac{3}{10}x - \frac{1}{14}$. 27. Group like terms: $$\left(\frac{1}{5}x + \frac{3}{10}x\right) + \left(-\frac{4}{7} - \frac{1}{14}\right)$$ 28. Find common denominators and add: $$\frac{1}{5}x = \frac{2}{10}x$$ $$\frac{2}{10}x + \frac{3}{10}x = \frac{5}{10}x = \frac{1}{2}x$$ 29. For constants: $$-\frac{4}{7} = -\frac{8}{14}$$ $$-\frac{8}{14} - \frac{1}{14} = -\frac{9}{14}$$ 30. Final answer: $\frac{1}{2}x - \frac{9}{14}$ 31. Problem: Simplify $\frac{3}{8}z + \frac{5}{6} + \frac{2}{3} - \frac{3}{4}z$. 32. Group like terms: $$\left(\frac{3}{8}z - \frac{3}{4}z\right) + \left(\frac{5}{6} + \frac{2}{3}\right)$$ 33. Simplify $z$ terms: $$\frac{3}{4}z = \frac{6}{8}z$$ $$\frac{3}{8}z - \frac{6}{8}z = -\frac{3}{8}z$$ 34. Simplify constants: $$\frac{2}{3} = \frac{4}{6}$$ $$\frac{5}{6} + \frac{4}{6} = \frac{9}{6} = \frac{3}{2}$$ 35. Final answer: $-\frac{3}{8}z + \frac{3}{2}$ 36. Problem: Simplify $\frac{3}{8} - \frac{1}{3}y + \frac{4}{5}y + \frac{1}{16}$. 37. Group like terms: $$\left(-\frac{1}{3}y + \frac{4}{5}y\right) + \left(\frac{3}{8} + \frac{1}{16}\right)$$ 38. Simplify $y$ terms: $$-\frac{1}{3}y = -\frac{5}{15}y$$ $$\frac{4}{5}y = \frac{12}{15}y$$ $$-\frac{5}{15}y + \frac{12}{15}y = \frac{7}{15}y$$ 39. Simplify constants: $$\frac{3}{8} = \frac{6}{16}$$ $$\frac{6}{16} + \frac{1}{16} = \frac{7}{16}$$ 40. Final answer: $\frac{7}{15}y + \frac{7}{16}$ 41. Problem: Simplify $\frac{1}{2}b + \frac{7}{8} - \frac{5}{8}b + \frac{1}{4}$. 42. Group like terms: $$\left(\frac{1}{2}b - \frac{5}{8}b\right) + \left(\frac{7}{8} + \frac{1}{4}\right)$$ 43. Simplify $b$ terms: $$\frac{1}{2}b = \frac{4}{8}b$$ $$\frac{4}{8}b - \frac{5}{8}b = -\frac{1}{8}b$$ 44. Simplify constants: $$\frac{1}{4} = \frac{2}{8}$$ $$\frac{7}{8} + \frac{2}{8} = \frac{9}{8}$$ 45. Final answer: $-\frac{1}{8}b + \frac{9}{8}$ 46. Problem: Simplify $-\frac{3}{5} - \frac{4}{5}a + \frac{3}{10}a - \frac{9}{10}$. 47. Group like terms: $$\left(-\frac{4}{5}a + \frac{3}{10}a\right) + \left(-\frac{3}{5} - \frac{9}{10}\right)$$ 48. Simplify $a$ terms: $$-\frac{4}{5}a = -\frac{8}{10}a$$ $$-\frac{8}{10}a + \frac{3}{10}a = -\frac{5}{10}a = -\frac{1}{2}a$$ 49. Simplify constants: $$-\frac{3}{5} = -\frac{6}{10}$$ $$-\frac{6}{10} - \frac{9}{10} = -\frac{15}{10} = -\frac{3}{2}$$ 50. Final answer: $-\frac{1}{2}a - \frac{3}{2}$ 51. Problem: Use the distributive property to expand $5(2x - 3)$. 52. Formula: $a(b + c) = ab + ac$ 53. Work: $$5 \times 2x - 5 \times 3 = 10x - 15$$ 54. Final answer: $10x - 15$ 55. Problem: Use the distributive property to expand $(-4y - 5z)3$. 56. Work: $$-4y \times 3 - 5z \times 3 = -12y - 15z$$ 57. Final answer: $-12y - 15z$ 58. Problem: Use the distributive property to expand $4(3x + 4y)$. 59. Work: $$4 \times 3x + 4 \times 4y = 12x + 16y$$ 60. Final answer: $12x + 16y$ 61. Problem: Use the distributive property to expand $-2(-3x - 2)$. 62. Work: $$-2 \times -3x - 2 \times -2 = 6x + 4$$ 63. Final answer: $6x + 4$ 64. Problem: Use the distributive property to expand $8(-2z + 1)$. 65. Work: $$8 \times -2z + 8 \times 1 = -16z + 8$$ 66. Final answer: $-16z + 8$ 67. Problem: Use the distributive property to expand $(4x - 6)2$. 68. Work: $$4x \times 2 - 6 \times 2 = 8x - 12$$ 69. Final answer: $8x - 12$ 70. Problem: Use the distributive property to expand $9(5y + 2)$. 71. Work: $$9 \times 5y + 9 \times 2 = 45y + 18$$ 72. Final answer: $45y + 18$ 73. Problem: Use the distributive property to expand $(-5x + 7)5$. 74. Work: $$-5x \times 5 + 7 \times 5 = -25x + 35$$ 75. Final answer: $-25x + 35$ 76. Problem: Use the distributive property to expand $-6(3y - 7z)$. 77. Work: $$-6 \times 3y - (-6) \times 7z = -18y + 42z$$ 78. Final answer: $-18y + 42z$