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CAPITULO VIII

Ecuaciones enteras de primer grado
Ejercicio 80
Resolver las siguientes ecuaciones:
  1. x+3(x1 ) =64(2x+3 ) x+3x3 =68x12 4x3 =68x 4x+8x =36 12x =3 x = 3 x = 1 4
  2. 5(x1 ) +16(2x+3 ) =3(2x7 ) x 5x5+32x+48 =6x21x 37x+43 =5x21 37x5x =4321 32x =64 x = 32 x =2
  3. 2(3x+3 ) 4(5x3 ) =x(x3 ) x(x+5 ) 6x+620x+12 = x 2 3x x 2 5x 14x+18 =8x 14x+8x =18 6x =18 x = 6 x =3
  4. 1847(2x+5 ) =301+6(x1 ) 6 18414x35 =301+6x66 14x+149 =289+6x 14x6x =289149 20x =140 x = 20 x =7
  5. 7(18x ) 6(35x ) =(7x+9 ) 3(2x+5 ) 12 1267x18+30x =7x96x1512 23x+108 =13x36 23x+13x =10836 36x =144 x = 36 x =4
  6. 3x(x3 ) +5(x+7 ) x(x+1 ) 2( x 2 +7 ) +4 =0 3 x 2 9x+5x+35 x 2 x 2 x 2 14+4 =0 5x+25 =0 5x =25 x = 5 x =5
  7. 3(2x+7 ) +(5x+6 ) 8(12x ) (x3 ) =0 6x215x+68+16xx+3 =0 4x20 =0 4x =20 x = 4 x =5
  8. (3x4 ) (4x3 ) =(6x4 ) (2x5 ) 12 x 2 9x16x+12 = 12 x 2 30x8x+20 25x+12 =38x+20 38x25x =2012 13x =8 x = 8 13
  9. (45x ) (4x5 ) =(10x3 ) (72x ) 16x20 20 x 2 +25x =70x 20 x 2 21+6x 41x20 =76x21 41x76x =2021 35x =1 x = 1 35
  10. (x+1 ) (2x+5 ) =(2x+3 ) (x4 ) +5 2 x 2 +5x+2x+5 = 2 x 2 8x+3x12+5 7x+5 =5x7 7x+5x =75 12x =12 x = 12 12 x =1
  11. (x2 ) 2 (3x ) 2 =1 [(x2 ) +(3x ) ] [(x2 ) (3x ) ] =1 [ x 2+3 x ] [x23+x ] =1 2x5 =1 2x =5+1 x = 2 x =3
  12. 14(5x1 ) (2x+3 ) =17(10x+1 ) (x6 ) 14(10 x 2 +15x2x3 ) =17(10 x 2 60x+x6 ) 14 10 x 2 15x+2x+3 =17 10 x 2 +60xx+6 13x+17 =59x+23 13x59x =2317 72x =6 x = 6 x = 1 12
  13. (x2 ) 2 +x(x3 ) =3(x+4 ) (x3 ) (x+2 ) (x1 ) +2 x 2 4x+4+ x 2 3x =3( x 2 +x12 ) ( x 2 +x2 ) +2 2 x 2 7x+ 4 =3 x 2 +3x36 x 2 x+ 2 + 2 2 x 2 7x = 2 x 2 +2x36 7x2x =36 9x =36 x = 9 x =4
  14. (3x1 ) 2 5(x2 ) (2x+3 ) 2 (5x+2 ) (x1 ) =0 9 x 2 6x+15x+10(4 x 2 +12x+9 ) (5 x 2 5x+2x2 ) =0 9 x 2 11x+11 4 x 2 12x9 5 x 2 +3x+2 =0 20x+4 =0 x = 4 x = 1 5
  15. 2 (x3 ) 2 3 (x+1 ) 2 +(x5 ) (x3 ) +4( x 2 5x+1 ) =4 x 2 12 2( x 2 6x+9 ) 3( x 2 +2x+1 ) +( x 2 8x+15 ) + 4 x 2 20x+4 = 4 x 2 12 2 x 2 12x+18 3 x 2 6x3+ x 2 8x+1520x+4 =12 46x+34 =12 46x =3412 x = 46 46 x =1
  16. 5 (x2 ) 2 5 (x+3 ) 2 +(2x1 ) (5x+2 ) 10 x 2 =0 5( x 2 4x+4 ) 5( x 2 +6x+9 ) +(10 x 2 +4x5x2 ) 10 x 2 =0 5 x 2 20x+20 5 x 2 30x45+ 10 x 2 x2 10 x 2 =0 51x27 =0 51x =27 x = x = 9 17
  17. x 2 5x+15 =x(x3 ) 14+5(x2 ) +3(132x ) x 2 5x+15 = x 2 3x14+5x10+396x 5x+ 15 =4x+ 15 5x+4x =0 x =0 x =0
  18. 3(5x6 ) (3x+2 ) 6(3x+4 ) (x1 ) 3(9x+1 ) (x2 ) =0 Dividiendo la ecuación para 3 (5x6 ) (3x+2 ) 2(3x+4 ) (x1 ) (9x+1 ) (x2 ) =0 (15 x 2 +10x18x12 ) 2(3 x 2 3x+4x4 ) (9 x 2 18x+x2 ) =0 15 x 2 8x12 6 x 2 2x+8 9 x 2 +17x+2 =0 7x2 =0 7x =2 x = 2 7
  19. 7 (x4 ) 2 3 (x+5 ) 2 =4(x+1 ) (x1 ) 2 7( x 2 8x+16 ) 3( x 2 +10x+25 ) =4( x 2 1 ) 2 7 x 2 56x+1123 x 2 30x75 =4 x 2 42 4 x 2 86x+37 = 4 x 2 6 86x =376 86x =43 x = 43 x = 1 2
  20. 5 (1x ) 2 6( x 2 3x7 ) =x(x3 ) 2x(x+5 ) 2 5(12x+ x 2 ) 6 x 2 +18x+42 = x 2 3x2 x 2 10x2 510x+5 x 2 6 x 2 +18x+42 = x 2 13x2 x 2 +8x+47 = x 2 13x2 8x+13x =472 21x =49 x = x = 7 3