Ejercicio 81

CAPITULO VIII

Ecuaciones enteras de primer grado
Ejercicio 81
MISCELANIA
Resolver las siguientes ecuaciones:
  1. 14x(3x2 ) [5x+2(x1 ) ] =0 14x3x+2[5x+2x+1 ] =0 11x+2(4x+3 ) =0 11x+24x3 =0 7x1 =0 7x =1 x = 1 7
  2. (3x7 ) 2 5(2x+1 ) (x2 ) = x 2 [(3x+1 ) ] 9 x 2 42x+495(2 x 2 4x+x2 ) = x 2 +(3x+1 ) 9 x 2 42x+4910 x 2 +15x+10 = x 2 +3x+1 x 2 27x+59 = x 2 +3x+1 27x3x =59+1 30x =58 x = x = 29 15
  3. 6x(2x+1 ) ={5x+[(2x1 ) ] } 6x2x1 ={5x+[2x+1 ] } 4x1 ={5x+2x+1 } 4x1 ={3x+1 } 4x 1 =3x 1 4x3x =0 x =0
  4. 2x+3( x 2 1 ) ={3 x 2 +2(x1 ) 3(x+2 ) } 2x3 x 2 3 ={3 x 2 +2x23x6 } 2x3 x 2 3 ={3 x 2 x8 } 2x 3 x 2 3 = 3 x 2 +x+8 2xx =8+3 x =11
  5. x 2 {3x+[x(x+1 ) +4( x 2 1 ) 4 x 2 ] } =0 x 2 {3x+[ x 2 +x+ 4 x 2 4 4 x 2 ] } =0 x 2 {3x+ x 2 +x4 } =0 x 2 { x 2 +4x4 } =0 x 2 x 2 4x+4 =0 4x =4 x = 4 4 x =1
  6. 3(2x+1 ) (x+3 ) (2x+5 ) 2 =[{3(x+5 ) } +10 x 2 ] 3(2 x 2 +6xx+3 ) (4 x 2 +20x+25 ) =[{3x15 } +10 x 2 ] 6 x 2 +15x+94 x 2 20x25 =[3x+15+10 x 2 ] 10 x 2 5x16 =3x15 10 x 2 5x+3x =1615 2x =1 x = 1 2
  7. (x+1 ) (x+2 ) (x3 ) =(x2 ) (x+1 ) (x+1 ) ( x 2 +3x+2 ) (x3 ) =( x 2 x2 ) (x+1 ) x 3 + 3 x 2 +2x 3 x 2 9x6 = x 3 x 2 2x+ x 2 x2 7x6 =3x2 7x+3x =62 4x =4 x = 4 4 x =1
  8. (x+2 ) (x+3 ) (x1 ) =(x+4 ) (x+4 ) (x4 ) +7 ( x 2 +5x+6 ) (x1 ) =(x+4 ) ( x 2 16 ) +7 x 3 +5 x 2 +6x x 2 5x6 = x 3 16x+4 x 2 64+7 4 x 2 +x6 = 4 x 2 16x+ 4 x 2 57 x+16x =657 17x =51 x = 17 x =3
  9. (x+1 ) 3 (x1 ) 3 =6x(x3 ) [(x+1 ) (x1 ) ] [ (x+1 ) 2 +(x+1 ) (x1 ) + (x1 ) 2 ] =6 x 2 18x [ x +1 x +1 ] [ x 2 + 2x + 1 + x 2 1 + x 2 2x +1 ] =6 x 2 18x 2(3 x 2 +1 ) =6 x 2 18x 6 x 2 +2 = 6 x 2 18x 2 =x x = 1 9
  10. 3 (x2 ) 2 (x+5 ) =3 (x+1 ) 2 (x1 ) +3 Dividiendo la ecuación para 3 (x2 ) 2 (x+5 ) = (x+1 ) 2 (x1 ) +1 ( x 2 4x+4 ) (x+5 ) =( x 2 +2x+1 ) (x1 ) +1 x 3 4 x 2 +4x+5 x 2 20x+20 = x 3 +2 x 2 +x x 2 2x 1 + 1 x 2 16x+20 = x 2 x 16x+x =20 15x =20 x = x = 4 3

Ejercicio 80

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

Ejercicio 79

CAPITULO VIII

Ecuaciones enteras de primer grado
Ejercicio 79
Resolver las siguientes ecuaciones:
  1. x(2x+1 ) =8(3x+3 ) x2x1 =83x3 x1 =3x+5 x+3x =5+1 2x =6 x = 2 x =3
  2. 15x10 =6x(x+2 ) +(x+3 ) 15x10 =6xx2x+3 15x10 =4x+1 15x4x =10+1 11x =11 x = 11 11 x =1
  3. (53x ) (4x+6 ) =(8x+11 ) (3x6 ) 53x+4x6 =8x+113x+6 x1 =5x+17 x5x =17+1 4x =18 x = x = 9 2
  4. 30x(x+6 ) +(5x+4 ) =(5x+6 ) +(8+3x ) 30x+x65x+4 =5x68+3x 26x2 =2x14 26x+2x =214 28x =12 x = x = 3 7
  5. 15x+(6x+5 ) 2(x+3 ) =(7x+23 ) x+(32x ) 15x6x+ 5 2 +x 3 =7x23x+32x 10x =10x20 10x+10x =20 20x =20 x = 20 20 x =1
  6. 3x+[5x(x+3 ) ] =8x+(5x9 ) 3x+[5xx3 ] =8x5x9 3x5xx3 =3x9 3x =3x9+3 3x3x =6 6x =6 x = 6 6 x =1
  7. 16x[3x(69x ) ] =30x+[(3x+2 ) (x+3 ) ] 16x[3x6+9x ] =30x+[3x2x3 ] 16x12x+6 =30x4x5 4x+6 =26x5 4x26x =65 22x =11 x = 11 x = 1 2
  8. x[5+3x{5x(6+x ) } ] =3 x[5+3x{5x6x } ] =3 x[5+3x4x+6 ] =3 x(11x ) =3 x11+x =3 2x =113 2x =8 x = 2 x =4
  9. 9x(5x+1 ) {2+8x(7x5 ) } +9x =0 18x5x1{2+8x7x+5 } =0 13x1(x+7 ) =0 13x1x7 =0 12x8 =0 12x =8 x = x = 2 3
  10. 71+[5x+(2x+3 ) ] =25[(3x+4 ) (4x+3 ) ] 71+[5x2x+3 ] =25[3x44x3 ] 717x+3 =25(7x7 ) 747x =25+7x+7 7x7x =3274 14x =42 x = 14 x =3
  11. {3x+8[15+6x(3x+2 ) (5x+4 ) ] 29 } =5 {3x+8[15+6x+3x25x4 ] 29 } =5 {3x+8[4x21 ] 29 } =5 {3x+ 8 4x+ 21 29 } =5 {x } =5 x =5

Ejercicio 78

CAPITULO VIII

Ecuaciones enteras de primer grado
Ejercicio 78
Resolver las ecuaciones:
  1. 5x =8x15 5x8x =15 3x =15 x = 3 x =5
  2. 4x+1 =2 4x =21 x = 1 4
  3. y5 =3y25 y3y =25+5 2y =20 y = 2 y =10
  4. 5x+6 =10x+5 5x10x =6+5 5x =1 x = 1 5
  5. 9y11 =10+12y 9y12y =10+11 3y =1 y = 1 3
  6. 216x =278x 6x+8x =2721 2x =6 x = 2 x =3
  7. 11x+5x1 =65x36 16x65x =36+1 49x =35 x = x = 5 7
  8. 8x4+3x =7x+x+14 11x8x =14+4 3x =18 x = 3 x =6
  9. 8x+912x =4x135x 4x+x =139 3x =22 x = 22 3
  10. 5y+6y81 =7y+102+65y 11y72y =102+81 61y =183 y = 61 y =3
  11. 16+7x5+x =11x3x 8x10x =311 2x =12 x = 2 x =7
  12. 3x+1014x33 =10816x100 x+68 =816x x+16x =868 15x =60 x = 15 x =4
  13. 1412x+39x18x =25660x657x 14+9x =256717x 9x+717x =25614 726x =242 x = 242 x = 1 3
  14. 8x15x30x51x =53x+31x172 88x =84x172 88x84x =172 172x =172 x = 172 172 x =1