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Ejercicio 80

Gestor Baldor
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CAPITULO VIII

Ecuaciones enteras de primer grado
Ejercicio 80
Resolver las siguientes ecuaciones:
  1. x+3( x–1 ) =6–4( 2x+3 ) x+3x–3 =6–8x–12 4x–3 =–6–8x 4x+8x =3–6 12x =–3 x =– 3 x =– 1 4
  2. 5( x–1 ) +16( 2x+3 ) =3( 2x–7 ) –x 5x–5+32x+48 =6x–21–x 37x+43 =5x–21 37x–5x =–43–21 32x =–64 x =– 32 x =–2
  3. 2( 3x+3 ) –4( 5x–3 ) =x( x–3 ) –x( x+5 ) 6x+6–20x+12 = x 2 –3x– x 2 –5x –14x+18 =–8x –14x+8x =–18 –6x =–18 x = – – 6 x =3
  4. 184–7( 2x+5 ) =301+6( x–1 ) –6 184–14x–35 =301+6x–6–6 –14x+149 =289+6x –14x–6x =289–149 –20x =140 x =– 20 x =–7
  5. 7( 18–x ) –6( 3–5x ) =–( 7x+9 ) –3( 2x+5 ) –12 126–7x–18+30x =–7x–9–6x–15–12 23x+108 =–13x–36 23x+13x =–108–36 36x =–144 x = – 36 x =–4
  6. 3x( x–3 ) +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( 1–2x ) –( x–3 ) =0 –6x–21–5x+6–8+16x–x+3 =0 4x–20 =0 4x =20 x = 4 x =5
  8. ( 3x–4 ) ( 4x–3 ) =( 6x–4 ) ( 2x–5 ) 12 x 2 –9x–16x+12 = 12 x 2 –30x–8x+20 –25x+12 =–38x+20 38x–25x =20–12 13x =8 x = 8 13
  9. ( 4–5x ) ( 4x–5 ) =( 10x–3 ) ( 7–2x ) 16x–20– 20 x 2 +25x =70x– 20 x 2 –21+6x 41x–20 =76x–21 41x–76x =20–21 –35x =–1 x = 1 35
  10. ( x+1 ) ( 2x+5 ) =( 2x+3 ) ( x–4 ) +5 2 x 2 +5x+2x+5 = 2 x 2 –8x+3x–12+5 7x+5 =–5x–7 7x+5x =–7–5 12x =–12 x =– 12 12 x =–1
  11. ( x–2 ) 2 – ( 3–x ) 2 =1 [ ( x–2 ) +( 3–x ) ] [ ( x–2 ) –( 3–x ) ] =1 [ x –2+3– x ] [ x–2–3+x ] =1 2x–5 =1 2x =5+1 x = 2 x =3
  12. 14–( 5x–1 ) ( 2x+3 ) =17–( 10x+1 ) ( x–6 ) 14–( 10 x 2 +15x–2x–3 ) =17–( 10 x 2 –60x+x–6 ) 14– 10 x 2 –15x+2x+3 =17– 10 x 2 +60x–x+6 –13x+17 =59x+23 –13x–59x =23–17 –72x =6 x =– 6 x =– 1 12
  13. ( x–2 ) 2 +x( x–3 ) =3( x+4 ) ( x–3 ) –( x+2 ) ( x–1 ) +2 x 2 –4x+4+ x 2 –3x =3( x 2 +x–12 ) –( x 2 +x–2 ) +2 2 x 2 –7x+ 4 =3 x 2 +3x–36– x 2 –x+ 2 + 2 2 x 2 –7x = 2 x 2 +2x–36 –7x–2x =–36 –9x =–36 x = – – 9 x =4
  14. ( 3x–1 ) 2 –5( x–2 ) – ( 2x+3 ) 2 –( 5x+2 ) ( x–1 ) =0 9 x 2 –6x+1–5x+10–( 4 x 2 +12x+9 ) –( 5 x 2 –5x+2x–2 ) =0 9 x 2 –11x+11– 4 x 2 –12x–9– 5 x 2 +3x+2 =0 –20x+4 =0 x = – 4 – x = 1 5
  15. 2 ( x–3 ) 2 –3 ( x+1 ) 2 +( x–5 ) ( x–3 ) +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 –6x–3+ x 2 –8x+15–20x+4 =–12 –46x+34 =–12 –46x =–34–12 x = – 46 – 46 x =1
  16. 5 ( x–2 ) 2 –5 ( x+3 ) 2 +( 2x–1 ) ( 5x+2 ) –10 x 2 =0 5( x 2 –4x+4 ) –5( x 2 +6x+9 ) +( 10 x 2 +4x–5x–2 ) –10 x 2 =0 5 x 2 –20x+20– 5 x 2 –30x–45+ 10 x 2 –x–2– 10 x 2 =0 –51x–27 =0 –51x =27 x =– x =– 9 17
  17. x 2 –5x+15 =x( x–3 ) –14+5( x–2 ) +3( 13–2x ) x 2 –5x+15 = x 2 –3x–14+5x–10+39–6x –5x+ 15 =–4x+ 15 –5x+4x =0 –x =0 x =0
  18. 3( 5x–6 ) ( 3x+2 ) –6( 3x+4 ) ( x–1 ) –3( 9x+1 ) ( x–2 ) =0 Dividiendo la ecuación para 3 ( 5x–6 ) ( 3x+2 ) –2( 3x+4 ) ( x–1 ) –( 9x+1 ) ( x–2 ) =0 ( 15 x 2 +10x–18x–12 ) –2( 3 x 2 –3x+4x–4 ) –( 9 x 2 –18x+x–2 ) =0 15 x 2 –8x–12– 6 x 2 –2x+8– 9 x 2 +17x+2 =0 7x–2 =0 7x =2 x = 2 7
  19. 7 ( x–4 ) 2 –3 ( x+5 ) 2 =4( x+1 ) ( x–1 ) –2 7( x 2 –8x+16 ) –3( x 2 +10x+25 ) =4( x 2 –1 ) –2 7 x 2 –56x+112–3 x 2 –30x–75 =4 x 2 –4–2 4 x 2 –86x+37 = 4 x 2 –6 –86x =–37–6 –86x =–43 x = – 43 – x = 1 2
  20. 5 ( 1–x ) 2 –6( x 2 –3x–7 ) =x( x–3 ) –2x( x+5 ) –2 5( 1–2x+ x 2 ) –6 x 2 +18x+42 = x 2 –3x–2 x 2 –10x–2 5–10x+5 x 2 –6 x 2 +18x+42 =– x 2 –13x–2 – x 2 +8x+47 =– x 2 –13x–2 8x+13x =–47–2 21x =–49 x =– x =– 7 3
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