41.  . Please do the following calculation. You need to simplify your answer.  15x   ÷  ( - 3/5) = _____*1 point2525x-525x-25x42. Please do the following calculation.       8 (3a – 5b) = ______*1 point16ab24ab24a-40b8a - 15b43. Please do the following calculation.                        -3(a-4b) = _____*1 point12ab12-4b-12b + 3a-3a + 12b44.  Please do the following calculation. You need to simplify your answer   -2 ( a/4 - 5/6 ) *1 point-a/2 + 5/33/10 a-10a / 2 + 3/5a/2 - 5/645. Please solve the following equation.       x – 8 = 1*1 point-98x-7946. Please solve the following equation.       7 + x = 5 *1 point2122x-247. Please solve the following equation.       x + 9 = 3 *1 point116-6-1148. Please solve the following equation.      –8 = 12 + x *1 point420-4-2049. Please solve the following equation.      - 2x = 5x – 28*1 point7x = -282825x450. Please solve the following equation.       3x -19 = 5 + 6x*1 point-8827-2751. Please solve the following equation.      -8x + 4 = – 13x – 16*1 point21x -2-2120-452. Please solve the following equation.       2x = - 6 *1 point23-3-253. Please solve the following equation.       2x = -18 *1 point9-920-2054. Please solve the following equation.     4x = - 5*1 point4/5-4/55/4-1 1/455. Please solve the following equation.       9x = - 3*1 point-3-1/331/356. Please solve the following equation.        -4( - x + 3) = 6( - 7x – 2)*1 point321057. Please solve the following equation.        2x – 3.5 = 1.4x – 5.3 *1 point-3.52.8-3358. Please solve the following equation.        0.3 (x – 2) = 0.1 (4 + x)*1 point54.432.459.  Please solve the following equation.       1/2 x ( X-5 ) - 3/5 x ( X-2) = 2.4 *1 point3845-37-4360.  Please solve the following equation.  (x+ S )  / 6  - ( x+5 ) / 5 = 0.2 *1 point-11s -135s-36-3636.02 + 5s

41. $15x \div \left( -\frac{3}{5} \right) = 15x \times \left( -\frac{5}{3} \right) = -25x$

42. $8(3a - 5b) = 24a - 40b$

43. $-3(a - 4b) = -3a + 12b$

44. $-2 \left( \frac{a}{4} - \frac{5}{6} \right) = -2 \left( \frac{3a - 10}{12} \right) = -\frac{3a}{2} + \frac{5}{3}$

45. $x - 8 = 1 \implies x = 9$

46. $7 + x = 5 \implies x = -2$

47. $x + 9 = 3 \implies x = -6$

48. $-8 = 12 + x \implies x = -20$

49. $-2x = 5x - 28 \implies -7x = -28 \implies x = 4$

50. $3x - 19 = 5 + 6x \implies -3x = 24 \implies x = -8$

51. $-8x + 4 = -13x - 16 \implies 5x = -20 \implies x = -4$

52. $2x = -6 \implies x = -3$

53. $2x = -18 \implies x = -9$

54. $4x = -5 \implies x = -\frac{5}{4}$

55. $9x = -3 \implies x = -\frac{1}{3}$

56. $-4(-x + 3) = 6(-7x - 2) \implies 4x - 12 = -42x - 12 \implies 46x = 0 \implies x = 0$

57. $2x - 3.5 = 1.4x - 5.3 \implies 0.6x = -1.8 \implies x = -3$

58. $0.3(x - 2) = 0.1(4 + x) \implies 0.3x - 0.6 = 0.1x + 0.4 \implies 0.2x = 1 \implies x = 5$

59. $\frac{1}{2}x(x - 5) - \frac{3}{5}x(x - 2) = 2.4 \implies \frac{5x^2 - 25x - 6x^2 + 12x}{10} = 2.4 \implies -\frac{x^2 + 13x}{10} = 2.4 \implies -x^2 - 13x = 24 \implies x^2 + 13x + 24 = 0 \implies (x + 3)(x + 8) = 0 \implies x = -3 \text{ or } x = -8$

60. $\frac{x + 5}{6} - \frac{x + 5}{5} = 0.2 \implies \frac{5(x + 5) - 6(x + 5)}{30} = 0.2 \implies \frac{-x - 5}{30} = 0.2 \implies -x - 5 = 6 \implies x = -11$

41. Para resolver $15x \div \left( -\frac{3}{5} \right)$:

Primero, recordemos que dividir por una fracción es lo mismo que multiplicar por su recíproco: $15x \div \left( -\frac{3}{5} \right) = 15x \times \left( -\frac{5}{3} \right)$

Multiplicamos: $15x \times \left( -\frac{5}{3} \right) = 15x \times -\frac{5}{3} = -25x$

Respuesta: $-25x$

42. Para resolver $8(3a - 5b)$:

Distribuimos el 8: $8 \times 3a - 8 \times 5b = 24a - 40b$

Respuesta: $24a - 40b$

43. Para resolver $-3(a - 4b)$:

Distribuimos el -3: $-3 \times a - (-3) \times 4b = -3a + 12b$

Respuesta: $-3a + 12b$

44. Para resolver $-2 \left( \frac{a}{4} - \frac{5}{6} \right)$:

Distribuimos el -2: $-2 \times \frac{a}{4} - (-2) \times \frac{5}{6} = -\frac{2a}{4} + \frac{10}{6} = -\frac{a}{2} + \frac{5}{3}$

Respuesta: $-\frac{a}{2} + \frac{5}{3}$

45. Para resolver $x - 8 = 1$:

Sumamos 8 a ambos lados: $x - 8 + 8 = 1 + 8$ $x = 9$

Respuesta: $9$

46. Para resolver $7 + x = 5$:

Restamos 7 a ambos lados: $7 + x - 7 = 5 - 7$ $x = -2$

Respuesta: $-2$

47. Para resolver $x + 9 = 3$:

Restamos 9 a ambos lados: $x + 9 - 9 = 3 - 9$ $x = -6$

Respuesta: $-6$

48. Para resolver $-8 = 12 + x$:

Restamos 12 a ambos lados: $-8 - 12 = 12 + x - 12$ $-20 = x$

Respuesta: $-20$

49. Para resolver $-2x = 5x - 28$:

Sumamos 2x a ambos lados: $-2x + 2x = 5x - 28 + 2x$ $0 = 7x - 28$

Sumamos 28 a ambos lados: $28 = 7x$

Dividimos entre 7: $x = 4$

Respuesta: $4$

50. Para resolver $3x - 19 = 5 + 6x$:

Restamos 3x a ambos lados: $3x - 19 - 3x = 5 + 6x - 3x$ $-19 = 5 + 3x$

Restamos 5 a ambos lados: $-19 - 5 = 5 - 5 + 3x$ $-24 = 3x$

Dividimos entre 3: $x = -8$

Respuesta: $-8$

51. Para resolver $-8x + 4 = -13x - 16$:

Sumamos 13x a ambos lados: $-8x + 13x + 4 = -13x + 13x - 16$ $5x + 4 = -16$

Restamos 4 a ambos lados: $5x + 4 - 4 = -16 - 4$ $5x = -20$

Dividimos entre 5: $x = -4$

Respuesta: $-4$

52. Para resolver $2x = -6$:

Dividimos entre 2: $x = -3$

Respuesta: $-3$

53. Para resolver $2x = -18$:

Dividimos entre 2: $x = -9$

Respuesta: $-9$

54. Para resolver $4x = -5$:

Dividimos entre 4: $x = -\frac{5}{4}$

Respuesta: $-\frac{5}{4}$

55. Para resolver $9x = -3$:

Dividimos entre 9: $x = -\frac{3}{9} = -\frac{1}{3}$

Respuesta: $-\frac{1}{3}$

56. Para resolver $-4(-x + 3) = 6(-7x - 2)$:

Distribuimos: $4x - 12 = -42x - 12$

Sumamos 42x a ambos lados: $4x + 42x - 12 = -42x + 42x - 12$ $46x - 12 = -12$

Sumamos 12 a ambos lados: $46x - 12 + 12 = -12 + 12$ $46x = 0$

Dividimos entre 46: $x = 0$

Respuesta: $0$

57. Para resolver $2x - 3.5 = 1.4x - 5.3$:

Restamos 1.4x a ambos lados: $2x - 1.4x - 3.5 = 1.4x - 1.4x - 5.3$ $0.6x - 3.5 = -5.3$

Sumamos 3.5 a ambos lados: $0.6x - 3.5 + 3.5 = -5.3 + 3.5$ $0.6x = -1.8$

Dividimos entre 0.6: $x = -3$

Respuesta: $-3$

58. Para resolver $0.3(x - 2) = 0.1(4 + x)$:

Distribuimos: $0.3x - 0.6 = 0.4 + 0.1x$

Restamos 0.1x a ambos lados: $0.3x - 0.1x - 0.6 = 0.4 + 0.1x - 0.1x$ $0.2x - 0.6 = 0.4$

Sumamos 0.6 a ambos lados: $0.2x - 0.6 + 0.6 = 0.4 + 0.6$ $0.2x = 1$

Dividimos entre 0.2: $x = 5$

Respuesta: $5$

59. Para resolver $\frac{1}{2}x(x - 5) - \frac{3}{5}x(x - 2) = 2.4$:

Multiplicamos y simplificamos: $\frac{1}{2}x^2 - \frac{5}{2}x - \frac{3}{5}x^2 + \frac{6}{5}x = 2.4$

Combinamos términos semejantes: $\left( \frac{1}{2} - \frac{3}{5} \right)x^2 + \left( -\frac{5}{2} + \frac{6}{5} \right)x = 2.4$

Convertimos a fracciones comunes: $\left( \frac{5}{10} - \frac{6}{10} \right)x^2 + \left( -\frac{25}{10} + \frac{12}{10} \right)x = 2.4$ $-\frac{1}{10}x^2 - \frac{13}{10}x = 2.4$

Multiplicamos todo por 10 para eliminar fracciones: $-x^2 - 13x = 24$

Multiplicamos por -1: $x^2 + 13x = -24$

Resolviendo la ecuación cuadrática: $x = \frac{-13 \pm \sqrt{13^2 - 4 \cdot 1 \cdot (-24)}}{2 \cdot 1}$ $x = \frac{-13 \pm \sqrt{169 + 96}}{2}$ $x = \frac{-13 \pm \sqrt{265}}{2}$

Respuesta: $x = \frac{-13 \pm \sqrt{265}}{2}$

60. Para resolver $\frac{x + 5}{6} - \frac{x + 5}{5} = 0.2$:

Multiplicamos todo por 30 para eliminar fracciones: $5(x + 5) - 6(x + 5) = 6$

Distribuimos: $5x + 25 - 6x - 30 = 6$

Simplificamos: $-x - 5 = 6$

Sumamos 5 a ambos lados: $-x - 5 + 5 = 6 + 5$ $-x = 11$

Multiplicamos por -1: $x = -11$

Respuesta: $-11$