Equacions

Troba el valor de "X"

Exercici 1

  1. \(8x - 5x = x + 8\)
  2. \(5x - 7 = 2 - 4x\)
  3. \(4x + 7 - x = 5 + 2x\)
  4. \(3x + 6 = 2x + 13\)
  5. \(3x + x + 4 = 2x + 10\)
  6. \(8 - x = 3x + 2x + 5\)
  7. \(6x - 9 + 3x - 2 - 5x = x - 6 - 3x + 1\)
  8. \(12x - 7 + x - 5 = 11x - 10 + x\)
  9. \(18x + 15 + 5x - 9 - 7x = 9x - 8\)
  10. \(7x - 3 + 5x - 4 = 8x - 5 - x\)
  11. \(10x + 1 - 7x = 5x - 5 + 4x\)
  12. \(2x - 5 - 7x + 1 = 4x - 6x + 11\)
  13. \(2 - 13x = 6x + 1 + x - 9\)
  14. \(2x + 5 - 3x = x + 19\)
  15. \(7x - 2x = 2x + 1 + 3x\)
  16. \(11 + 2x = 6x - 3 + 3x\)
  17. \(7 + 5x - 2 = x - 3 + 2x\)
  18. \(x - 1 - 4x = 5 - 3x - 6\)
  19. \(3x - x + 7x + 12 = 3x + 9\)
  20. \(5x - 7 + 2x = 3x - 3 + 4x - 5\)
Solucions
  1. \(x = 4\)
  2. \(x = 1\)
  3. \(x = -2\)
  4. \(x = 7\)
  5. \(x = 3\)
  6. \(x = \tfrac12\)
  7. \(x = 1\)
  8. \(x = 2\)
  9. \(x = -2\)
  10. \(x = \tfrac{2}{5}\)
  11. \(x = 1\)
  12. \(x = -5\)
  13. \(x = \tfrac12\)
  14. \(x = -7\)
  15. No solució
  16. \(x = 2\)
  17. \(x = -4\)
  18. Identitat
  19. \(x = -\tfrac12\)
  20. No solució

Exercici 2

  1. \(7x + 3 - 8x = 2x + 4 - 6x\)
  2. \(7x - (1 - x) = x - 8\)
  3. \(5 - (4x + 6) = 2x\)
  4. \(x + 1 = 5x - (2x + 3)\)
  5. \(2x - (5 - 4x) + 1 = x + (3x - 5)\)
  6. \(5 - (x + 1) - 3 = 3x - (2x + 3) - x\)
  7. \(4 - x = 2 - 3(x - 2)\)
  8. \(x - 2(x - 2) = 3x\)
  9. \(11 - x = 3x - 5(2x - 1)\)
  10. \(x - 4(x + 2) = x + 5 - 3x\)
  11. \(4(x - 2) + 3 = 1 - 3(2 - x)\)
  12. \(2x - 8 = 1 - 3(x - 2)\)
  13. \(4x - (2 + x) = 3(x - 1)\)
  14. \(2x + 3(x + 1) = 5 - 2(2x - 5)\)
  15. \(2x - 3(5x + 6) + 10 = 5(x - 3) - 4x\)
  16. \(3(1 - 4x) + 7 = 5 - (8x + 7)\)
  17. \(12 - 5(3 - 2x) = 8x - 3(x + 1) + 5x\)
  18. \(x - (3 - x) = 7 - (x - 2)\)
  19. \(3x - (1 + 5x) = 9 - (2x + 7) - x\)
  20. \((2x - 5) - (5x + 1) = 8x - (2 + 7x)\)
Solucions
  1. \(x = \tfrac13\)
  2. \(x = -1\)
  3. \(x = -\tfrac16\)
  4. \(x = 2\)
  5. \(x = -\tfrac12\)
  6. \(x = 4\)
  7. \(x = 2\)
  8. \(x = 1\)
  9. \(x = -1\)
  10. \(x = -13\)
  11. \(x = 0\)
  12. \(x = 3\)
  13. No solució
  14. \(x = \tfrac{4}{3}\)
  15. \(x = \tfrac12\)
  16. \(x = 3\)
  17. Identitat
  18. \(x = 4\)
  19. \(x = 3\)
  20. \(x = -1\)

Exercici 3

  1. \(\dfrac{x}{5} + 1 = 7\)
  2. \(\dfrac{3x}{5} + 10 = x\)
  3. \(\dfrac{x}{3} - \dfrac{7}{2} = \dfrac{5}{2}\)
  4. \(\dfrac{2x}{3} - \dfrac{x}{2} = \dfrac{x}{6}\)
  5. \(\dfrac{x - 5}{3} = \dfrac{x - 5}{2}\)
  6. \(\dfrac{2x - 5}{5} = \dfrac{1 + 2x}{2}\)
  7. \(\dfrac{x - 5}{2} = \dfrac{8 - x}{4}\)
  8. \(\dfrac{x}{2} + \dfrac{x}{5} - \dfrac{3x}{7} = 38\)
  9. \(\dfrac{2x}{5} - x = 12 - 3x\)
  10. \(\dfrac{2x - 7}{3} + 3 = 1 - x\)
  11. \(\dfrac{x}{2} + x - 21 = \dfrac{x}{4} + \dfrac{x}{5}\)
  12. \(\dfrac{x}{2} - \dfrac{3x}{4} = 5 - \dfrac{2x}{3}\)
  13. \(1 - \dfrac{4}{7}x = 4 - x\)
  14. \(\dfrac{5x}{3} + 1 = \dfrac{1}{3} - \dfrac{x}{6}\)
  15. \(\dfrac{2}{3} + \dfrac{x}{2} - \dfrac{3x}{4} = \dfrac{1}{2}\)
  16. \(\dfrac{x - 11}{6} - \dfrac{x - 5}{9} = 4x - 2\)
  17. \(\dfrac{2x - 4}{3} + \dfrac{3x + 6}{2} = x - 2\)
  18. \(\dfrac{7 - 5x}{3} = \dfrac{13 - 3x}{2} - 11\)
  19. \(\dfrac{x}{12} - \dfrac{x + 16}{10} = 22 - x\)
  20. \(\dfrac{x}{2} + \dfrac{x - 3}{3} + \dfrac{x - 4}{4} = 13\)
Solucions
  1. x = 30
  2. x = 25
  3. x = 18
  4. Identitat
  5. x = 5
  6. x = -5/2
  7. x = 6
  8. x = 140
  9. x = 5
  10. x = 1/5
  11. x = 20
  12. x = 12
  13. x = 7
  14. x = -4/11
  15. x = 2/3
  16. x = 13/71
  17. x = -22/7
  18. x = 41
  19. x = 24
  20. x = 180/13

Exercici 4

  1. \(\dfrac{x+5}{8} - \dfrac{x-1}{10} = -\dfrac{x+1}{12}\)
  2. \(\dfrac{x-4}{3} - \dfrac{5x-1}{2} = \dfrac{2x+1}{6}\)
  3. \(\dfrac{2x - 4}{3} - \dfrac{3x + 6}{2} = x - 2\)
  4. \(\dfrac{3x}{4} + 3x = 3\!\left(\dfrac{x}{2} - 1\right)\)
  5. \(\dfrac{2(x-3)}{3} - \dfrac{6(2-x)}{5} = 0\)
  6. \(\dfrac{2(3-x)}{3} - \dfrac{4(x-2)}{5} = 8\)
  7. \(\dfrac{2(x+3)}{9} - \dfrac{4x - 9}{15} = 1\)
  8. \(2(x-7) - \dfrac{x+3}{4} = x - 5\)
  9. \(\dfrac{3(x-1)}{2} - \dfrac{5(3-x)}{4} = 2x\)
  10. \(\dfrac{2(x-2)}{3} - x + 2 = \dfrac{3(-x-2)}{5}\)
  11. \(\dfrac{1}{3} - \dfrac{4(x-5)}{3} - \dfrac{3x}{4} = \dfrac{1}{2} - \dfrac{2(x+3)}{3}\)
  12. \(\dfrac{x}{5} - 2\!\left(\dfrac{x}{7} - \dfrac{1}{5}\right) = 3x\)
  13. \(3\!\left(\dfrac{x}{2} - 5\right) = \dfrac{3}{2}(3x - 2)\)
  14. \(\dfrac{3x}{4} + 1 = 3\!\left(\dfrac{3x}{2} - \dfrac{x}{3}\right)\)
  15. \(\dfrac{x + 5}{3} + 2\!\left(\dfrac{3x}{2} - x\right) = -1\)
  16. \(5\!\left(\dfrac{x}{3} - \dfrac{3}{4}\right) = 9\!\left(5 - \dfrac{2x}{3}\right)\)
  17. \(3\!\left(\dfrac{5x}{3} + 1\right) = 2\!\left(\dfrac{1}{3} - \dfrac{x}{5}\right)\)
  18. \(\dfrac{5x}{3} - 3\!\left(\dfrac{x}{4} + \dfrac{4}{5}\right) = 3\!\left(\dfrac{1}{5} - \dfrac{2x}{3}\right) - 38\)
  19. \(\dfrac{5x - 4}{3} + 3\!\left(\dfrac{x}{2} + 1\right) = 2\!\left(4 + \dfrac{3x}{2}\right)\)
Solucions
  1. x = -97/13
  2. x = -2/5
  3. x = -14/11
  4. x = -4/3
  5. x = 33/14
  6. x = -3
  7. x = 6
  8. x = 13
  9. x = 7
  10. x = -7
  11. x = 6
  12. x = 7/54
  13. x = -4
  14. x = 4/11
  15. x = -2
  16. x = 195/34
  17. x = -35/81
  18. x = -12
  19. x = 38