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Ejercicio 164

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CAPITULO XIX

Inecuaciones
Ejercicio 164
Hallar el límite de x en las inecuaciones siguientes:
  1. x–5 <2x–6 x–2x <–6+5 –x <–1 x >1
  2. 5x–12 >3x–4 5x–3x >12–4 2x >8 x > 2 x >4
  3. x–6 >21–8x x+8x >21+6 9x >27 x > 9 x >3
  4. 3x–14 <7x–2 3x–7x <14–2 –4x <12 x >– 4 x >–3
  5. 2x– 5 3 > x 3 +10 2x– x 3 >10+ 5 3 6x–x 3 > 30+5 3 5x >35 x > 5 x >7
  6. 3x–4+ x 4 < 5x 2 +2 3x+ x 4 – 5x 2 <4+2 12x+x–10x 4 <6 3x 4 <6 x < 4 3 x <8
  7. ( x–1 ) 2 –7 > ( x–2 ) 2 ( x–1 ) 2 – ( x–2 ) 2 >7 [ ( x–1 ) +( x–2 ) ] [ ( x–1 ) –( x–2 ) ] >7 [ x–1+x–2 ] [ x–1–x+2 ] >7 [ 2x–3 ] [ x –1– x +2 ] >7 2x–3 >7 2x >7+3 x > 2 x >5
  8. ( x+2 ) ( x–1 ) +26 <( x+4 ) ( x+5 ) x 2 +x–2+26 < x 2 +9x+20 x–9x <20–24 –8x <–4 8x >4 x > 4 x > 1 2
  9. 3( x–2 ) +2x( x+3 ) >( 2x–1 ) ( x+4 ) 3x–6+ 2 x 2 +6x > 2 x 2 +8x–x–4 9x–6 >7x–4 9x–7x >6–4 2x >2 x > 2 2 x >1
  10. 6( x 2 +1 ) –( 2x–4 ) ( 3x+2 ) <3( 5x+21 ) 6 x 2 +6–( 6 x 2 +4x–12x–8 ) <15x+63 6 x 2 +6– 6 x 2 –4x+12x+8 <15x+63 8x+14 <15x+63 8x–15x <63–14 –7x <49 x >– 7 x >–7
  11. ( x–4 ) ( x+5 ) <( x–3 ) ( x–2 ) x 2 +x–20 < x 2 –5x+6 x+5x <20+6 6x <26 x < x < 13 3
  12. ( 2x–3 ) 2 +4 x 2 ( x–7 ) <4 ( x–2 ) 3 4 x 2 –12x+9+4 x 3 –28 x 2 <4( x 2 –4x+4 ) ( x–2 ) 4 x 3 –24 x 2 –12x+9 <4( x 3 –4 x 2 +4x–2 x 2 +8x–8 ) 4 x 3 –24 x 2 –12x+9 <4( x 3 –6 x 2 +12x–8 ) 4 x 3 – 24 x 2 –12x+9 < 4 x 3 – 24 x 2 +48x–32 –12x–48x <–9–32 –60x <–41 60x >41 x > 41 60
  13. 2x+1 3x–1 > 2x+5 3x+2 ( 2x+1 ) ( 3x+2 ) >( 2x+5 ) ( 3x–1 ) 6 x 2 +4x+3x+2 > 6 x 2 –2x+15x–5 7x+2 >13x–5 7x–13x >–2–5 –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+6–12 > x 2 +2x 5x–2x >6 3x >6 x > 3 x >2
  15. 5 3x+1 – 20 9 x 2 –1 < 2 3x–1 5 3x+1 – 20 ( 3x+1 ) ( 3x–1 ) < 2 3x–1 5( 3x–1 ) –20 ( 3x+1 ) ( 3x–1 ) < 2 3x–1 5( 3x–1 ) –20 <2( 3x+1 ) 15x–5–20 <6x+2 15x–25 <6x+2 15x–6x <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( x–1 ) – 1 ( x–1 ) ( x+1 ) 1 x( x+1 ) > x +1– x x( x+1 ) ( x–1 ) 1 > 1 x–1 x–1 >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 2x–3x 6 >–14 –x >6( –14 ) x <84 Números enteros menores que 84
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