Ejercicio 164

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CAPITULO XIX

Inecuaciones
Ejercicio 164
Hallar el límite de x en las inecuaciones siguientes:
  1. x5 <2x6 x2x <6+5 x <1 x >1
  2. 5x12 >3x4 5x3x >124 2x >8 x > 2 x >4
  3. x6 >218x x+8x >21+6 9x >27 x > 9 x >3
  4. 3x14 <7x2 3x7x <142 4x <12 x > 4 x >3
  5. 2x 5 3 > x 3 +10 2x x 3 >10+ 5 3 6xx 3 > 30+5 3 5x >35 x > 5 x >7
  6. 3x4+ x 4 < 5x 2 +2 3x+ x 4 5x 2 <4+2 12x+x10x 4 <6 3x 4 <6 x < 4 3 x <8
  7. (x1 ) 2 7 > (x2 ) 2 (x1 ) 2 (x2 ) 2 >7 [(x1 ) +(x2 ) ] [(x1 ) (x2 ) ] >7 [x1+x2 ] [x1x+2 ] >7 [2x3 ] [ x 1 x +2 ] >7 2x3 >7 2x >7+3 x > 2 x >5
  8. (x+2 ) (x1 ) +26 <(x+4 ) (x+5 ) x 2 +x2+26 < x 2 +9x+20 x9x <2024 8x <4 8x >4 x > 4 x > 1 2
  9. 3(x2 ) +2x(x+3 ) >(2x1 ) (x+4 ) 3x6+ 2 x 2 +6x > 2 x 2 +8xx4 9x6 >7x4 9x7x >64 2x >2 x > 2 2 x >1
  10. 6( x 2 +1 ) (2x4 ) (3x+2 ) <3(5x+21 ) 6 x 2 +6(6 x 2 +4x12x8 ) <15x+63 6 x 2 +6 6 x 2 4x+12x+8 <15x+63 8x+14 <15x+63 8x15x <6314 7x <49 x > 7 x >7
  11. (x4 ) (x+5 ) <(x3 ) (x2 ) x 2 +x20 < x 2 5x+6 x+5x <20+6 6x <26 x < x < 13 3
  12. (2x3 ) 2 +4 x 2 (x7 ) <4 (x2 ) 3 4 x 2 12x+9+4 x 3 28 x 2 <4( x 2 4x+4 ) (x2 ) 4 x 3 24 x 2 12x+9 <4( x 3 4 x 2 +4x2 x 2 +8x8 ) 4 x 3 24 x 2 12x+9 <4( x 3 6 x 2 +12x8 ) 4 x 3 24 x 2 12x+9 < 4 x 3 24 x 2 +48x32 12x48x <932 60x <41 60x >41 x > 41 60
  13. 2x+1 3x1 > 2x+5 3x+2 (2x+1 ) (3x+2 ) >(2x+5 ) (3x1 ) 6 x 2 +4x+3x+2 > 6 x 2 2x+15x5 7x+2 >13x5 7x13x >25 6x >7 6x <7 x < 7 6
  14. x+3 3 4 x+2 > x 3 (x+2 ) (x+3 ) 12 3 (x+2 ) > x 3 (x+2 ) (x+3 ) 12 >x(x+2 ) x 2 +5x+612 > x 2 +2x 5x2x >6 3x >6 x > 3 x >2
  15. 5 3x+1 20 9 x 2 1 < 2 3x1 5 3x+1 20 (3x+1 ) (3x1 ) < 2 3x1 5(3x1 ) 20 (3x+1 )(3x1 ) < 2 3x1 5(3x1 ) 20 <2(3x+1 ) 15x520 <6x+2 15x25 <6x+2 15x6x <25+2 9x <27 x < 9 x <3
  16. 1 x 2 +x > 1 x 2 x 1 x 2 1 1 x(x+1 ) > 1 x(x1 ) 1 (x1 ) (x+1 ) 1 x(x+1 ) > x +1 x x(x+1 ) (x1 ) 1 > 1 x1 x1 >1 x >1+1 x >2
  17. Hallar los números cuyo tercio aumentado en 15 sea mayor que su mitad aumentada en 1
    x  números enteros x 3 +15 > x 2 +1 x 3 x 2 >15+1 2x3x 6 >14 x >6(14 ) x <84 Números enteros menores que 84