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- Sistemas de desigualdades paso a paso
- Ecuaciones básicas paso a paso
- Sistemas de ecuaciones paso a paso
- Solución de desigualdades trigonométricas en línea
- Resolución de desigualdades exponenciales en línea
- Resolución de desigualdades con un módulo en línea
-
¿Cómo usar?
- Desigualdades:
-
x^2+4x-21>0
-
(2-x)*(3x+5)*(x^2-x+1)>0
-
x^2+2x-3<0
-
(x-1)*(x-2)<0
- Forma canónica:
- =0
-
Expresiones idénticas
- cuarenta y cinco ^x- veintisiete ^x- dieciocho * quince ^x+ dos * nueve ^(x+ uno)+ ochenta y uno * cinco ^x- tres ^(x+ cuatro)<= cero
- 45 en el grado x menos 27 en el grado x menos 18 multiplicar por 15 en el grado x más 2 multiplicar por 9 en el grado (x más 1) más 81 multiplicar por 5 en el grado x menos 3 en el grado (x más 4) menos o igual a 0
- cuarenta y cinco en el grado x menos veintisiete en el grado x menos dieciocho multiplicar por quince en el grado x más dos multiplicar por nueve en el grado (x más uno) más ochenta y uno multiplicar por cinco en el grado x menos tres en el grado (x más cuatro) menos o igual a cero
- 45x-27x-18*15x+2*9(x+1)+81*5x-3(x+4)<=0
- 45x-27x-18*15x+2*9x+1+81*5x-3x+4<=0
- 45^x-27^x-1815^x+29^(x+1)+815^x-3^(x+4)<=0
- 45x-27x-1815x+29(x+1)+815x-3(x+4)<=0
- 45x-27x-1815x+29x+1+815x-3x+4<=0
- 45^x-27^x-1815^x+29^x+1+815^x-3^x+4<=0
- 45^x-27^x-18*15^x+2*9^(x+1)+81*5^x-3^(x+4)<=O
-
Expresiones semejantes
- 45^x-27^x+18*15^x+2*9^(x+1)+81*5^x-3^(x+4)<=0
- 45^x-27^x-18*15^x+2*9^(x+1)+81*5^x+3^(x+4)<=0
- 45^x-27^x-18*15^x+2*9^(x+1)-81*5^x-3^(x+4)<=0
- 45^x-27^x-18*15^x+2*9^(x-1)+81*5^x-3^(x+4)<=0
- 45^x-27^x-18*15^x-2*9^(x+1)+81*5^x-3^(x+4)<=0
- 45^x-27^x-18*15^x+2*9^(x+1)+81*5^x-3^(x-4)<=0
- 45^x+27^x-18*15^x+2*9^(x+1)+81*5^x-3^(x+4)<=0
45^x-27^x-18*15^x+2*9^(x+1)+81*5^x-3^(x+4)<=0 desigualdades
Solución
Ha introducido
[src]
x x x x + 1 x x + 4 45 - 27 - 18*15 + 2*9 + 81*5 - 3 <= 0
$$- 3^{x + 4} + \left(81 \cdot 5^{x} + \left(2 \cdot 9^{x + 1} + \left(- 18 \cdot 15^{x} + \left(- 27^{x} + 45^{x}\right)\right)\right)\right) \leq 0$$
-3^(x + 4) + 81*5^x + 2*9^(x + 1) - 18*15^x - 27^x + 45^x <= 0
Solución detallada
Se da la desigualdad:
$$- 3^{x + 4} + \left(81 \cdot 5^{x} + \left(2 \cdot 9^{x + 1} + \left(- 18 \cdot 15^{x} + \left(- 27^{x} + 45^{x}\right)\right)\right)\right) \leq 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$- 3^{x + 4} + \left(81 \cdot 5^{x} + \left(2 \cdot 9^{x + 1} + \left(- 18 \cdot 15^{x} + \left(- 27^{x} + 45^{x}\right)\right)\right)\right) = 0$$
Resolvemos:
$$x_{1} = -82.9855570613729$$
$$x_{2} = -64.9855570614493$$
$$x_{3} = -80.9855570613729$$
$$x_{4} = -116.985557061373$$
$$x_{5} = -62.9855570615851$$
$$x_{6} = -36.9856814734066$$
$$x_{7} = -34.9859027016135$$
$$x_{8} = -58.9855570630103$$
$$x_{9} = -84.9855570613729$$
$$x_{10} = -42.9855628654895$$
$$x_{11} = -112.985557061373$$
$$x_{12} = -118.985557061373$$
$$x_{13} = -78.9855570613729$$
$$x_{14} = -28.9930026468386$$
$$x_{15} = -40.9855731840259$$
$$x_{16} = -88.9855570613729$$
$$x_{17} = -76.985557061373$$
$$x_{18} = -92.9855570613729$$
$$x_{19} = -104.985557061373$$
$$x_{20} = -30.9882283475395$$
$$x_{21} = -98.9855570613729$$
$$x_{22} = -108.985557061373$$
$$x_{23} = -60.9855570619623$$
$$x_{24} = -94.9855570613729$$
$$x_{25} = -44.98555915085$$
$$x_{26} = -32.9865175766309$$
$$x_{27} = -66.9855570614004$$
$$x_{28} = -48.9855573321688$$
$$x_{29} = 0$$
$$x_{30} = -46.985557813584$$
$$x_{31} = -74.9855570613733$$
$$x_{32} = -100.985557061373$$
$$x_{33} = -114.985557061373$$
$$x_{34} = -50.9855571588594$$
$$x_{35} = -106.985557061373$$
$$x_{36} = -102.985557061373$$
$$x_{37} = -110.985557061373$$
$$x_{38} = -56.9855570659212$$
$$x_{39} = -52.985557096468$$
$$x_{40} = -90.9855570613729$$
$$x_{41} = -70.9855570613764$$
$$x_{42} = -68.9855570613828$$
$$x_{43} = -96.9855570613729$$
$$x_{44} = 2$$
$$x_{45} = -38.9856018473541$$
$$x_{46} = -72.9855570613742$$
$$x_{47} = -54.9855570740071$$
$$x_{48} = -86.9855570613729$$
$$x_{1} = -82.9855570613729$$
$$x_{2} = -64.9855570614493$$
$$x_{3} = -80.9855570613729$$
$$x_{4} = -116.985557061373$$
$$x_{5} = -62.9855570615851$$
$$x_{6} = -36.9856814734066$$
$$x_{7} = -34.9859027016135$$
$$x_{8} = -58.9855570630103$$
$$x_{9} = -84.9855570613729$$
$$x_{10} = -42.9855628654895$$
$$x_{11} = -112.985557061373$$
$$x_{12} = -118.985557061373$$
$$x_{13} = -78.9855570613729$$
$$x_{14} = -28.9930026468386$$
$$x_{15} = -40.9855731840259$$
$$x_{16} = -88.9855570613729$$
$$x_{17} = -76.985557061373$$
$$x_{18} = -92.9855570613729$$
$$x_{19} = -104.985557061373$$
$$x_{20} = -30.9882283475395$$
$$x_{21} = -98.9855570613729$$
$$x_{22} = -108.985557061373$$
$$x_{23} = -60.9855570619623$$
$$x_{24} = -94.9855570613729$$
$$x_{25} = -44.98555915085$$
$$x_{26} = -32.9865175766309$$
$$x_{27} = -66.9855570614004$$
$$x_{28} = -48.9855573321688$$
$$x_{29} = 0$$
$$x_{30} = -46.985557813584$$
$$x_{31} = -74.9855570613733$$
$$x_{32} = -100.985557061373$$
$$x_{33} = -114.985557061373$$
$$x_{34} = -50.9855571588594$$
$$x_{35} = -106.985557061373$$
$$x_{36} = -102.985557061373$$
$$x_{37} = -110.985557061373$$
$$x_{38} = -56.9855570659212$$
$$x_{39} = -52.985557096468$$
$$x_{40} = -90.9855570613729$$
$$x_{41} = -70.9855570613764$$
$$x_{42} = -68.9855570613828$$
$$x_{43} = -96.9855570613729$$
$$x_{44} = 2$$
$$x_{45} = -38.9856018473541$$
$$x_{46} = -72.9855570613742$$
$$x_{47} = -54.9855570740071$$
$$x_{48} = -86.9855570613729$$
Las raíces dadas
$$x_{12} = -118.985557061373$$
$$x_{4} = -116.985557061373$$
$$x_{33} = -114.985557061373$$
$$x_{11} = -112.985557061373$$
$$x_{37} = -110.985557061373$$
$$x_{22} = -108.985557061373$$
$$x_{35} = -106.985557061373$$
$$x_{19} = -104.985557061373$$
$$x_{36} = -102.985557061373$$
$$x_{32} = -100.985557061373$$
$$x_{21} = -98.9855570613729$$
$$x_{43} = -96.9855570613729$$
$$x_{24} = -94.9855570613729$$
$$x_{18} = -92.9855570613729$$
$$x_{40} = -90.9855570613729$$
$$x_{16} = -88.9855570613729$$
$$x_{48} = -86.9855570613729$$
$$x_{9} = -84.9855570613729$$
$$x_{1} = -82.9855570613729$$
$$x_{3} = -80.9855570613729$$
$$x_{13} = -78.9855570613729$$
$$x_{17} = -76.985557061373$$
$$x_{31} = -74.9855570613733$$
$$x_{46} = -72.9855570613742$$
$$x_{41} = -70.9855570613764$$
$$x_{42} = -68.9855570613828$$
$$x_{27} = -66.9855570614004$$
$$x_{2} = -64.9855570614493$$
$$x_{5} = -62.9855570615851$$
$$x_{23} = -60.9855570619623$$
$$x_{8} = -58.9855570630103$$
$$x_{38} = -56.9855570659212$$
$$x_{47} = -54.9855570740071$$
$$x_{39} = -52.985557096468$$
$$x_{34} = -50.9855571588594$$
$$x_{28} = -48.9855573321688$$
$$x_{30} = -46.985557813584$$
$$x_{25} = -44.98555915085$$
$$x_{10} = -42.9855628654895$$
$$x_{15} = -40.9855731840259$$
$$x_{45} = -38.9856018473541$$
$$x_{6} = -36.9856814734066$$
$$x_{7} = -34.9859027016135$$
$$x_{26} = -32.9865175766309$$
$$x_{20} = -30.9882283475395$$
$$x_{14} = -28.9930026468386$$
$$x_{29} = 0$$
$$x_{44} = 2$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{12}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{12} - \frac{1}{10}$$
=
$$-118.985557061373 + - \frac{1}{10}$$
=
$$-119.085557061373$$
lo sustituimos en la expresión
$$- 3^{x + 4} + \left(81 \cdot 5^{x} + \left(2 \cdot 9^{x + 1} + \left(- 18 \cdot 15^{x} + \left(- 27^{x} + 45^{x}\right)\right)\right)\right) \leq 0$$
$$- 3^{-119.085557061373 + 4} + \left(\left(\left(- \frac{18}{15^{119.085557061373}} + \left(- \frac{1}{27^{119.085557061373}} + 45^{-119.085557061373}\right)\right) + 2 \cdot 9^{-119.085557061373 + 1}\right) + \frac{81}{5^{119.085557061373}}\right) \leq 0$$
significa que una de las soluciones de nuestra ecuación será con:
$$x \leq -118.985557061373$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \leq -118.985557061373$$
$$x \geq -116.985557061373 \wedge x \leq -114.985557061373$$
$$x \geq -112.985557061373 \wedge x \leq -110.985557061373$$
$$x \geq -108.985557061373 \wedge x \leq -106.985557061373$$
$$x \geq -104.985557061373 \wedge x \leq -102.985557061373$$
$$x \geq -100.985557061373 \wedge x \leq -98.9855570613729$$
$$x \geq -96.9855570613729 \wedge x \leq -94.9855570613729$$
$$x \geq -92.9855570613729 \wedge x \leq -90.9855570613729$$
$$x \geq -88.9855570613729 \wedge x \leq -86.9855570613729$$
$$x \geq -84.9855570613729 \wedge x \leq -82.9855570613729$$
$$x \geq -80.9855570613729 \wedge x \leq -78.9855570613729$$
$$x \geq -76.985557061373 \wedge x \leq -74.9855570613733$$
$$x \geq -72.9855570613742 \wedge x \leq -70.9855570613764$$
$$x \geq -68.9855570613828 \wedge x \leq -66.9855570614004$$
$$x \geq -64.9855570614493 \wedge x \leq -62.9855570615851$$
$$x \geq -60.9855570619623 \wedge x \leq -58.9855570630103$$
$$x \geq -56.9855570659212 \wedge x \leq -54.9855570740071$$
$$x \geq -52.985557096468 \wedge x \leq -50.9855571588594$$
$$x \geq -48.9855573321688 \wedge x \leq -46.985557813584$$
$$x \geq -44.98555915085 \wedge x \leq -42.9855628654895$$
$$x \geq -40.9855731840259 \wedge x \leq -38.9856018473541$$
$$x \geq -36.9856814734066 \wedge x \leq -34.9859027016135$$
$$x \geq -32.9865175766309 \wedge x \leq -30.9882283475395$$
$$x \geq -28.9930026468386 \wedge x \leq 0$$
$$x \geq 2$$
$$- 3^{x + 4} + \left(81 \cdot 5^{x} + \left(2 \cdot 9^{x + 1} + \left(- 18 \cdot 15^{x} + \left(- 27^{x} + 45^{x}\right)\right)\right)\right) \leq 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$- 3^{x + 4} + \left(81 \cdot 5^{x} + \left(2 \cdot 9^{x + 1} + \left(- 18 \cdot 15^{x} + \left(- 27^{x} + 45^{x}\right)\right)\right)\right) = 0$$
Resolvemos:
$$x_{1} = -82.9855570613729$$
$$x_{2} = -64.9855570614493$$
$$x_{3} = -80.9855570613729$$
$$x_{4} = -116.985557061373$$
$$x_{5} = -62.9855570615851$$
$$x_{6} = -36.9856814734066$$
$$x_{7} = -34.9859027016135$$
$$x_{8} = -58.9855570630103$$
$$x_{9} = -84.9855570613729$$
$$x_{10} = -42.9855628654895$$
$$x_{11} = -112.985557061373$$
$$x_{12} = -118.985557061373$$
$$x_{13} = -78.9855570613729$$
$$x_{14} = -28.9930026468386$$
$$x_{15} = -40.9855731840259$$
$$x_{16} = -88.9855570613729$$
$$x_{17} = -76.985557061373$$
$$x_{18} = -92.9855570613729$$
$$x_{19} = -104.985557061373$$
$$x_{20} = -30.9882283475395$$
$$x_{21} = -98.9855570613729$$
$$x_{22} = -108.985557061373$$
$$x_{23} = -60.9855570619623$$
$$x_{24} = -94.9855570613729$$
$$x_{25} = -44.98555915085$$
$$x_{26} = -32.9865175766309$$
$$x_{27} = -66.9855570614004$$
$$x_{28} = -48.9855573321688$$
$$x_{29} = 0$$
$$x_{30} = -46.985557813584$$
$$x_{31} = -74.9855570613733$$
$$x_{32} = -100.985557061373$$
$$x_{33} = -114.985557061373$$
$$x_{34} = -50.9855571588594$$
$$x_{35} = -106.985557061373$$
$$x_{36} = -102.985557061373$$
$$x_{37} = -110.985557061373$$
$$x_{38} = -56.9855570659212$$
$$x_{39} = -52.985557096468$$
$$x_{40} = -90.9855570613729$$
$$x_{41} = -70.9855570613764$$
$$x_{42} = -68.9855570613828$$
$$x_{43} = -96.9855570613729$$
$$x_{44} = 2$$
$$x_{45} = -38.9856018473541$$
$$x_{46} = -72.9855570613742$$
$$x_{47} = -54.9855570740071$$
$$x_{48} = -86.9855570613729$$
$$x_{1} = -82.9855570613729$$
$$x_{2} = -64.9855570614493$$
$$x_{3} = -80.9855570613729$$
$$x_{4} = -116.985557061373$$
$$x_{5} = -62.9855570615851$$
$$x_{6} = -36.9856814734066$$
$$x_{7} = -34.9859027016135$$
$$x_{8} = -58.9855570630103$$
$$x_{9} = -84.9855570613729$$
$$x_{10} = -42.9855628654895$$
$$x_{11} = -112.985557061373$$
$$x_{12} = -118.985557061373$$
$$x_{13} = -78.9855570613729$$
$$x_{14} = -28.9930026468386$$
$$x_{15} = -40.9855731840259$$
$$x_{16} = -88.9855570613729$$
$$x_{17} = -76.985557061373$$
$$x_{18} = -92.9855570613729$$
$$x_{19} = -104.985557061373$$
$$x_{20} = -30.9882283475395$$
$$x_{21} = -98.9855570613729$$
$$x_{22} = -108.985557061373$$
$$x_{23} = -60.9855570619623$$
$$x_{24} = -94.9855570613729$$
$$x_{25} = -44.98555915085$$
$$x_{26} = -32.9865175766309$$
$$x_{27} = -66.9855570614004$$
$$x_{28} = -48.9855573321688$$
$$x_{29} = 0$$
$$x_{30} = -46.985557813584$$
$$x_{31} = -74.9855570613733$$
$$x_{32} = -100.985557061373$$
$$x_{33} = -114.985557061373$$
$$x_{34} = -50.9855571588594$$
$$x_{35} = -106.985557061373$$
$$x_{36} = -102.985557061373$$
$$x_{37} = -110.985557061373$$
$$x_{38} = -56.9855570659212$$
$$x_{39} = -52.985557096468$$
$$x_{40} = -90.9855570613729$$
$$x_{41} = -70.9855570613764$$
$$x_{42} = -68.9855570613828$$
$$x_{43} = -96.9855570613729$$
$$x_{44} = 2$$
$$x_{45} = -38.9856018473541$$
$$x_{46} = -72.9855570613742$$
$$x_{47} = -54.9855570740071$$
$$x_{48} = -86.9855570613729$$
Las raíces dadas
$$x_{12} = -118.985557061373$$
$$x_{4} = -116.985557061373$$
$$x_{33} = -114.985557061373$$
$$x_{11} = -112.985557061373$$
$$x_{37} = -110.985557061373$$
$$x_{22} = -108.985557061373$$
$$x_{35} = -106.985557061373$$
$$x_{19} = -104.985557061373$$
$$x_{36} = -102.985557061373$$
$$x_{32} = -100.985557061373$$
$$x_{21} = -98.9855570613729$$
$$x_{43} = -96.9855570613729$$
$$x_{24} = -94.9855570613729$$
$$x_{18} = -92.9855570613729$$
$$x_{40} = -90.9855570613729$$
$$x_{16} = -88.9855570613729$$
$$x_{48} = -86.9855570613729$$
$$x_{9} = -84.9855570613729$$
$$x_{1} = -82.9855570613729$$
$$x_{3} = -80.9855570613729$$
$$x_{13} = -78.9855570613729$$
$$x_{17} = -76.985557061373$$
$$x_{31} = -74.9855570613733$$
$$x_{46} = -72.9855570613742$$
$$x_{41} = -70.9855570613764$$
$$x_{42} = -68.9855570613828$$
$$x_{27} = -66.9855570614004$$
$$x_{2} = -64.9855570614493$$
$$x_{5} = -62.9855570615851$$
$$x_{23} = -60.9855570619623$$
$$x_{8} = -58.9855570630103$$
$$x_{38} = -56.9855570659212$$
$$x_{47} = -54.9855570740071$$
$$x_{39} = -52.985557096468$$
$$x_{34} = -50.9855571588594$$
$$x_{28} = -48.9855573321688$$
$$x_{30} = -46.985557813584$$
$$x_{25} = -44.98555915085$$
$$x_{10} = -42.9855628654895$$
$$x_{15} = -40.9855731840259$$
$$x_{45} = -38.9856018473541$$
$$x_{6} = -36.9856814734066$$
$$x_{7} = -34.9859027016135$$
$$x_{26} = -32.9865175766309$$
$$x_{20} = -30.9882283475395$$
$$x_{14} = -28.9930026468386$$
$$x_{29} = 0$$
$$x_{44} = 2$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{12}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{12} - \frac{1}{10}$$
=
$$-118.985557061373 + - \frac{1}{10}$$
=
$$-119.085557061373$$
lo sustituimos en la expresión
$$- 3^{x + 4} + \left(81 \cdot 5^{x} + \left(2 \cdot 9^{x + 1} + \left(- 18 \cdot 15^{x} + \left(- 27^{x} + 45^{x}\right)\right)\right)\right) \leq 0$$
$$- 3^{-119.085557061373 + 4} + \left(\left(\left(- \frac{18}{15^{119.085557061373}} + \left(- \frac{1}{27^{119.085557061373}} + 45^{-119.085557061373}\right)\right) + 2 \cdot 9^{-119.085557061373 + 1}\right) + \frac{81}{5^{119.085557061373}}\right) \leq 0$$
-1.23093356673045e-55 <= 0
significa que una de las soluciones de nuestra ecuación será con:
$$x \leq -118.985557061373$$
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x12 x4 x33 x11 x37 x22 x35 x19 x36 x32 x21 x43 x24 x18 x40 x16 x48 x9 x1 x3 x13 x17 x31 x46 x41 x42 x27 x2 x5 x23 x8 x38 x47 x39 x34 x28 x30 x25 x10 x15 x45 x6 x7 x26 x20 x14 x29 x44Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \leq -118.985557061373$$
$$x \geq -116.985557061373 \wedge x \leq -114.985557061373$$
$$x \geq -112.985557061373 \wedge x \leq -110.985557061373$$
$$x \geq -108.985557061373 \wedge x \leq -106.985557061373$$
$$x \geq -104.985557061373 \wedge x \leq -102.985557061373$$
$$x \geq -100.985557061373 \wedge x \leq -98.9855570613729$$
$$x \geq -96.9855570613729 \wedge x \leq -94.9855570613729$$
$$x \geq -92.9855570613729 \wedge x \leq -90.9855570613729$$
$$x \geq -88.9855570613729 \wedge x \leq -86.9855570613729$$
$$x \geq -84.9855570613729 \wedge x \leq -82.9855570613729$$
$$x \geq -80.9855570613729 \wedge x \leq -78.9855570613729$$
$$x \geq -76.985557061373 \wedge x \leq -74.9855570613733$$
$$x \geq -72.9855570613742 \wedge x \leq -70.9855570613764$$
$$x \geq -68.9855570613828 \wedge x \leq -66.9855570614004$$
$$x \geq -64.9855570614493 \wedge x \leq -62.9855570615851$$
$$x \geq -60.9855570619623 \wedge x \leq -58.9855570630103$$
$$x \geq -56.9855570659212 \wedge x \leq -54.9855570740071$$
$$x \geq -52.985557096468 \wedge x \leq -50.9855571588594$$
$$x \geq -48.9855573321688 \wedge x \leq -46.985557813584$$
$$x \geq -44.98555915085 \wedge x \leq -42.9855628654895$$
$$x \geq -40.9855731840259 \wedge x \leq -38.9856018473541$$
$$x \geq -36.9856814734066 \wedge x \leq -34.9859027016135$$
$$x \geq -32.9865175766309 \wedge x \leq -30.9882283475395$$
$$x \geq -28.9930026468386 \wedge x \leq 0$$
$$x \geq 2$$
Solución de la desigualdad en el gráfico
Gráfico