Sr Examen
Otras calculadoras
- 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-7)(x+8)>0
-
-x^2-10x-24>0
-
4x-4>9x+6
-
3+x/4+2-x/3<0
- Forma canónica:
- =0
-
Expresiones idénticas
- dos * veinte ^x- diecisiete * diez ^x- dos * ocho ^x+ ocho * cinco ^x+ diecisiete * cuatro ^x- dos ^(x+ tres)<= cero
- 2 multiplicar por 20 en el grado x menos 17 multiplicar por 10 en el grado x menos 2 multiplicar por 8 en el grado x más 8 multiplicar por 5 en el grado x más 17 multiplicar por 4 en el grado x menos 2 en el grado (x más 3) menos o igual a 0
- dos multiplicar por veinte en el grado x menos diecisiete multiplicar por diez en el grado x menos dos multiplicar por ocho en el grado x más ocho multiplicar por cinco en el grado x más diecisiete multiplicar por cuatro en el grado x menos dos en el grado (x más tres) menos o igual a cero
- 2*20x-17*10x-2*8x+8*5x+17*4x-2(x+3)<=0
- 2*20x-17*10x-2*8x+8*5x+17*4x-2x+3<=0
- 220^x-1710^x-28^x+85^x+174^x-2^(x+3)<=0
- 220x-1710x-28x+85x+174x-2(x+3)<=0
- 220x-1710x-28x+85x+174x-2x+3<=0
- 220^x-1710^x-28^x+85^x+174^x-2^x+3<=0
- 2*20^x-17*10^x-2*8^x+8*5^x+17*4^x-2^(x+3)<=O
-
Expresiones semejantes
- 2*20^x+17*10^x-2*8^x+8*5^x+17*4^x-2^(x+3)<=0
- 2*20^x-17*10^x-2*8^x+8*5^x+17*4^x-2^(x-3)<=0
- 2*20^x-17*10^x-2*8^x-8*5^x+17*4^x-2^(x+3)<=0
- 2*20^x-17*10^x+2*8^x+8*5^x+17*4^x-2^(x+3)<=0
- 2*20^x-17*10^x-2*8^x+8*5^x-17*4^x-2^(x+3)<=0
- 2*20^x-17*10^x-2*8^x+8*5^x+17*4^x+2^(x+3)<=0
2*20^x-17*10^x-2*8^x+8*5^x+17*4^x-2^(x+3)<=0 desigualdades
Solución
Ha introducido
[src]
x x x x x x + 3 2*20 - 17*10 - 2*8 + 8*5 + 17*4 - 2 <= 0
$$- 2^{x + 3} + \left(17 \cdot 4^{x} + \left(8 \cdot 5^{x} + \left(- 2 \cdot 8^{x} + \left(- 17 \cdot 10^{x} + 2 \cdot 20^{x}\right)\right)\right)\right) \leq 0$$
-2^(x + 3) + 17*4^x + 8*5^x - 2*8^x - 17*10^x + 2*20^x <= 0
Solución detallada
Se da la desigualdad:
$$- 2^{x + 3} + \left(17 \cdot 4^{x} + \left(8 \cdot 5^{x} + \left(- 2 \cdot 8^{x} + \left(- 17 \cdot 10^{x} + 2 \cdot 20^{x}\right)\right)\right)\right) \leq 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$- 2^{x + 3} + \left(17 \cdot 4^{x} + \left(8 \cdot 5^{x} + \left(- 2 \cdot 8^{x} + \left(- 17 \cdot 10^{x} + 2 \cdot 20^{x}\right)\right)\right)\right) = 0$$
Resolvemos:
$$x_{1} = -70.1767600931369$$
$$x_{2} = -58.1767601130444$$
$$x_{3} = -92.176760093132$$
$$x_{4} = -82.176760093132$$
$$x_{5} = -78.176760093132$$
$$x_{6} = -74.1767600931323$$
$$x_{7} = -112.176760093132$$
$$x_{8} = -60.1767600981082$$
$$x_{9} = -88.176760093132$$
$$x_{10} = -108.176760093132$$
$$x_{11} = -104.176760093132$$
$$x_{12} = -96.176760093132$$
$$x_{13} = -90.176760093132$$
$$x_{14} = -122.176760093132$$
$$x_{15} = -114.176760093132$$
$$x_{16} = -64.1767600934429$$
$$x_{17} = -106.176760093132$$
$$x_{18} = -80.176760093132$$
$$x_{19} = -130.176760093132$$
$$x_{20} = -118.176760093132$$
$$x_{21} = -102.176760093132$$
$$x_{22} = -124.176760093132$$
$$x_{23} = -100.176760093132$$
$$x_{24} = -128.176760093132$$
$$x_{25} = -110.176760093132$$
$$x_{26} = -52.1767613713416$$
$$x_{27} = -46.1768428337543$$
$$x_{28} = -48.1767806640327$$
$$x_{29} = -44.1770939320033$$
$$x_{30} = -94.176760093132$$
$$x_{31} = -98.176760093132$$
$$x_{32} = -76.1767600931321$$
$$x_{33} = 0$$
$$x_{34} = -50.176765217626$$
$$x_{35} = -72.1767600931332$$
$$x_{36} = -120.176760093132$$
$$x_{37} = -56.1767601728291$$
$$x_{38} = 3$$
$$x_{39} = -84.176760093132$$
$$x_{40} = -54.1767604122184$$
$$x_{41} = -126.176760093132$$
$$x_{42} = -66.1767600932097$$
$$x_{43} = -68.1767600931515$$
$$x_{44} = -86.176760093132$$
$$x_{45} = -62.1767600943758$$
$$x_{46} = -116.176760093132$$
$$x_{1} = -70.1767600931369$$
$$x_{2} = -58.1767601130444$$
$$x_{3} = -92.176760093132$$
$$x_{4} = -82.176760093132$$
$$x_{5} = -78.176760093132$$
$$x_{6} = -74.1767600931323$$
$$x_{7} = -112.176760093132$$
$$x_{8} = -60.1767600981082$$
$$x_{9} = -88.176760093132$$
$$x_{10} = -108.176760093132$$
$$x_{11} = -104.176760093132$$
$$x_{12} = -96.176760093132$$
$$x_{13} = -90.176760093132$$
$$x_{14} = -122.176760093132$$
$$x_{15} = -114.176760093132$$
$$x_{16} = -64.1767600934429$$
$$x_{17} = -106.176760093132$$
$$x_{18} = -80.176760093132$$
$$x_{19} = -130.176760093132$$
$$x_{20} = -118.176760093132$$
$$x_{21} = -102.176760093132$$
$$x_{22} = -124.176760093132$$
$$x_{23} = -100.176760093132$$
$$x_{24} = -128.176760093132$$
$$x_{25} = -110.176760093132$$
$$x_{26} = -52.1767613713416$$
$$x_{27} = -46.1768428337543$$
$$x_{28} = -48.1767806640327$$
$$x_{29} = -44.1770939320033$$
$$x_{30} = -94.176760093132$$
$$x_{31} = -98.176760093132$$
$$x_{32} = -76.1767600931321$$
$$x_{33} = 0$$
$$x_{34} = -50.176765217626$$
$$x_{35} = -72.1767600931332$$
$$x_{36} = -120.176760093132$$
$$x_{37} = -56.1767601728291$$
$$x_{38} = 3$$
$$x_{39} = -84.176760093132$$
$$x_{40} = -54.1767604122184$$
$$x_{41} = -126.176760093132$$
$$x_{42} = -66.1767600932097$$
$$x_{43} = -68.1767600931515$$
$$x_{44} = -86.176760093132$$
$$x_{45} = -62.1767600943758$$
$$x_{46} = -116.176760093132$$
Las raíces dadas
$$x_{19} = -130.176760093132$$
$$x_{24} = -128.176760093132$$
$$x_{41} = -126.176760093132$$
$$x_{22} = -124.176760093132$$
$$x_{14} = -122.176760093132$$
$$x_{36} = -120.176760093132$$
$$x_{20} = -118.176760093132$$
$$x_{46} = -116.176760093132$$
$$x_{15} = -114.176760093132$$
$$x_{7} = -112.176760093132$$
$$x_{25} = -110.176760093132$$
$$x_{10} = -108.176760093132$$
$$x_{17} = -106.176760093132$$
$$x_{11} = -104.176760093132$$
$$x_{21} = -102.176760093132$$
$$x_{23} = -100.176760093132$$
$$x_{31} = -98.176760093132$$
$$x_{12} = -96.176760093132$$
$$x_{30} = -94.176760093132$$
$$x_{3} = -92.176760093132$$
$$x_{13} = -90.176760093132$$
$$x_{9} = -88.176760093132$$
$$x_{44} = -86.176760093132$$
$$x_{39} = -84.176760093132$$
$$x_{4} = -82.176760093132$$
$$x_{18} = -80.176760093132$$
$$x_{5} = -78.176760093132$$
$$x_{32} = -76.1767600931321$$
$$x_{6} = -74.1767600931323$$
$$x_{35} = -72.1767600931332$$
$$x_{1} = -70.1767600931369$$
$$x_{43} = -68.1767600931515$$
$$x_{42} = -66.1767600932097$$
$$x_{16} = -64.1767600934429$$
$$x_{45} = -62.1767600943758$$
$$x_{8} = -60.1767600981082$$
$$x_{2} = -58.1767601130444$$
$$x_{37} = -56.1767601728291$$
$$x_{40} = -54.1767604122184$$
$$x_{26} = -52.1767613713416$$
$$x_{34} = -50.176765217626$$
$$x_{28} = -48.1767806640327$$
$$x_{27} = -46.1768428337543$$
$$x_{29} = -44.1770939320033$$
$$x_{33} = 0$$
$$x_{38} = 3$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{19}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{19} - \frac{1}{10}$$
=
$$-130.176760093132 + - \frac{1}{10}$$
=
$$-130.276760093132$$
lo sustituimos en la expresión
$$- 2^{x + 3} + \left(17 \cdot 4^{x} + \left(8 \cdot 5^{x} + \left(- 2 \cdot 8^{x} + \left(- 17 \cdot 10^{x} + 2 \cdot 20^{x}\right)\right)\right)\right) \leq 0$$
$$- 2^{-130.276760093132 + 3} + \left(\left(\left(- \frac{2}{8^{130.276760093132}} + \left(- \frac{17}{10^{130.276760093132}} + \frac{2}{20^{130.276760093132}}\right)\right) + \frac{8}{5^{130.276760093132}}\right) + \frac{17}{4^{130.276760093132}}\right) \leq 0$$
significa que una de las soluciones de nuestra ecuación será con:
$$x \leq -130.176760093132$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \leq -130.176760093132$$
$$x \geq -128.176760093132 \wedge x \leq -126.176760093132$$
$$x \geq -124.176760093132 \wedge x \leq -122.176760093132$$
$$x \geq -120.176760093132 \wedge x \leq -118.176760093132$$
$$x \geq -116.176760093132 \wedge x \leq -114.176760093132$$
$$x \geq -112.176760093132 \wedge x \leq -110.176760093132$$
$$x \geq -108.176760093132 \wedge x \leq -106.176760093132$$
$$x \geq -104.176760093132 \wedge x \leq -102.176760093132$$
$$x \geq -100.176760093132 \wedge x \leq -98.176760093132$$
$$x \geq -96.176760093132 \wedge x \leq -94.176760093132$$
$$x \geq -92.176760093132 \wedge x \leq -90.176760093132$$
$$x \geq -88.176760093132 \wedge x \leq -86.176760093132$$
$$x \geq -84.176760093132 \wedge x \leq -82.176760093132$$
$$x \geq -80.176760093132 \wedge x \leq -78.176760093132$$
$$x \geq -76.1767600931321 \wedge x \leq -74.1767600931323$$
$$x \geq -72.1767600931332 \wedge x \leq -70.1767600931369$$
$$x \geq -68.1767600931515 \wedge x \leq -66.1767600932097$$
$$x \geq -64.1767600934429 \wedge x \leq -62.1767600943758$$
$$x \geq -60.1767600981082 \wedge x \leq -58.1767601130444$$
$$x \geq -56.1767601728291 \wedge x \leq -54.1767604122184$$
$$x \geq -52.1767613713416 \wedge x \leq -50.176765217626$$
$$x \geq -48.1767806640327 \wedge x \leq -46.1768428337543$$
$$x \geq -44.1770939320033 \wedge x \leq 0$$
$$x \geq 3$$
$$- 2^{x + 3} + \left(17 \cdot 4^{x} + \left(8 \cdot 5^{x} + \left(- 2 \cdot 8^{x} + \left(- 17 \cdot 10^{x} + 2 \cdot 20^{x}\right)\right)\right)\right) \leq 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$- 2^{x + 3} + \left(17 \cdot 4^{x} + \left(8 \cdot 5^{x} + \left(- 2 \cdot 8^{x} + \left(- 17 \cdot 10^{x} + 2 \cdot 20^{x}\right)\right)\right)\right) = 0$$
Resolvemos:
$$x_{1} = -70.1767600931369$$
$$x_{2} = -58.1767601130444$$
$$x_{3} = -92.176760093132$$
$$x_{4} = -82.176760093132$$
$$x_{5} = -78.176760093132$$
$$x_{6} = -74.1767600931323$$
$$x_{7} = -112.176760093132$$
$$x_{8} = -60.1767600981082$$
$$x_{9} = -88.176760093132$$
$$x_{10} = -108.176760093132$$
$$x_{11} = -104.176760093132$$
$$x_{12} = -96.176760093132$$
$$x_{13} = -90.176760093132$$
$$x_{14} = -122.176760093132$$
$$x_{15} = -114.176760093132$$
$$x_{16} = -64.1767600934429$$
$$x_{17} = -106.176760093132$$
$$x_{18} = -80.176760093132$$
$$x_{19} = -130.176760093132$$
$$x_{20} = -118.176760093132$$
$$x_{21} = -102.176760093132$$
$$x_{22} = -124.176760093132$$
$$x_{23} = -100.176760093132$$
$$x_{24} = -128.176760093132$$
$$x_{25} = -110.176760093132$$
$$x_{26} = -52.1767613713416$$
$$x_{27} = -46.1768428337543$$
$$x_{28} = -48.1767806640327$$
$$x_{29} = -44.1770939320033$$
$$x_{30} = -94.176760093132$$
$$x_{31} = -98.176760093132$$
$$x_{32} = -76.1767600931321$$
$$x_{33} = 0$$
$$x_{34} = -50.176765217626$$
$$x_{35} = -72.1767600931332$$
$$x_{36} = -120.176760093132$$
$$x_{37} = -56.1767601728291$$
$$x_{38} = 3$$
$$x_{39} = -84.176760093132$$
$$x_{40} = -54.1767604122184$$
$$x_{41} = -126.176760093132$$
$$x_{42} = -66.1767600932097$$
$$x_{43} = -68.1767600931515$$
$$x_{44} = -86.176760093132$$
$$x_{45} = -62.1767600943758$$
$$x_{46} = -116.176760093132$$
$$x_{1} = -70.1767600931369$$
$$x_{2} = -58.1767601130444$$
$$x_{3} = -92.176760093132$$
$$x_{4} = -82.176760093132$$
$$x_{5} = -78.176760093132$$
$$x_{6} = -74.1767600931323$$
$$x_{7} = -112.176760093132$$
$$x_{8} = -60.1767600981082$$
$$x_{9} = -88.176760093132$$
$$x_{10} = -108.176760093132$$
$$x_{11} = -104.176760093132$$
$$x_{12} = -96.176760093132$$
$$x_{13} = -90.176760093132$$
$$x_{14} = -122.176760093132$$
$$x_{15} = -114.176760093132$$
$$x_{16} = -64.1767600934429$$
$$x_{17} = -106.176760093132$$
$$x_{18} = -80.176760093132$$
$$x_{19} = -130.176760093132$$
$$x_{20} = -118.176760093132$$
$$x_{21} = -102.176760093132$$
$$x_{22} = -124.176760093132$$
$$x_{23} = -100.176760093132$$
$$x_{24} = -128.176760093132$$
$$x_{25} = -110.176760093132$$
$$x_{26} = -52.1767613713416$$
$$x_{27} = -46.1768428337543$$
$$x_{28} = -48.1767806640327$$
$$x_{29} = -44.1770939320033$$
$$x_{30} = -94.176760093132$$
$$x_{31} = -98.176760093132$$
$$x_{32} = -76.1767600931321$$
$$x_{33} = 0$$
$$x_{34} = -50.176765217626$$
$$x_{35} = -72.1767600931332$$
$$x_{36} = -120.176760093132$$
$$x_{37} = -56.1767601728291$$
$$x_{38} = 3$$
$$x_{39} = -84.176760093132$$
$$x_{40} = -54.1767604122184$$
$$x_{41} = -126.176760093132$$
$$x_{42} = -66.1767600932097$$
$$x_{43} = -68.1767600931515$$
$$x_{44} = -86.176760093132$$
$$x_{45} = -62.1767600943758$$
$$x_{46} = -116.176760093132$$
Las raíces dadas
$$x_{19} = -130.176760093132$$
$$x_{24} = -128.176760093132$$
$$x_{41} = -126.176760093132$$
$$x_{22} = -124.176760093132$$
$$x_{14} = -122.176760093132$$
$$x_{36} = -120.176760093132$$
$$x_{20} = -118.176760093132$$
$$x_{46} = -116.176760093132$$
$$x_{15} = -114.176760093132$$
$$x_{7} = -112.176760093132$$
$$x_{25} = -110.176760093132$$
$$x_{10} = -108.176760093132$$
$$x_{17} = -106.176760093132$$
$$x_{11} = -104.176760093132$$
$$x_{21} = -102.176760093132$$
$$x_{23} = -100.176760093132$$
$$x_{31} = -98.176760093132$$
$$x_{12} = -96.176760093132$$
$$x_{30} = -94.176760093132$$
$$x_{3} = -92.176760093132$$
$$x_{13} = -90.176760093132$$
$$x_{9} = -88.176760093132$$
$$x_{44} = -86.176760093132$$
$$x_{39} = -84.176760093132$$
$$x_{4} = -82.176760093132$$
$$x_{18} = -80.176760093132$$
$$x_{5} = -78.176760093132$$
$$x_{32} = -76.1767600931321$$
$$x_{6} = -74.1767600931323$$
$$x_{35} = -72.1767600931332$$
$$x_{1} = -70.1767600931369$$
$$x_{43} = -68.1767600931515$$
$$x_{42} = -66.1767600932097$$
$$x_{16} = -64.1767600934429$$
$$x_{45} = -62.1767600943758$$
$$x_{8} = -60.1767600981082$$
$$x_{2} = -58.1767601130444$$
$$x_{37} = -56.1767601728291$$
$$x_{40} = -54.1767604122184$$
$$x_{26} = -52.1767613713416$$
$$x_{34} = -50.176765217626$$
$$x_{28} = -48.1767806640327$$
$$x_{27} = -46.1768428337543$$
$$x_{29} = -44.1770939320033$$
$$x_{33} = 0$$
$$x_{38} = 3$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{19}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{19} - \frac{1}{10}$$
=
$$-130.176760093132 + - \frac{1}{10}$$
=
$$-130.276760093132$$
lo sustituimos en la expresión
$$- 2^{x + 3} + \left(17 \cdot 4^{x} + \left(8 \cdot 5^{x} + \left(- 2 \cdot 8^{x} + \left(- 17 \cdot 10^{x} + 2 \cdot 20^{x}\right)\right)\right)\right) \leq 0$$
$$- 2^{-130.276760093132 + 3} + \left(\left(\left(- \frac{2}{8^{130.276760093132}} + \left(- \frac{17}{10^{130.276760093132}} + \frac{2}{20^{130.276760093132}}\right)\right) + \frac{8}{5^{130.276760093132}}\right) + \frac{17}{4^{130.276760093132}}\right) \leq 0$$
-4.85151592228788e-39 <= 0
significa que una de las soluciones de nuestra ecuación será con:
$$x \leq -130.176760093132$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------
x19 x24 x41 x22 x14 x36 x20 x46 x15 x7 x25 x10 x17 x11 x21 x23 x31 x12 x30 x3 x13 x9 x44 x39 x4 x18 x5 x32 x6 x35 x1 x43 x42 x16 x45 x8 x2 x37 x40 x26 x34 x28 x27 x29 x33 x38Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \leq -130.176760093132$$
$$x \geq -128.176760093132 \wedge x \leq -126.176760093132$$
$$x \geq -124.176760093132 \wedge x \leq -122.176760093132$$
$$x \geq -120.176760093132 \wedge x \leq -118.176760093132$$
$$x \geq -116.176760093132 \wedge x \leq -114.176760093132$$
$$x \geq -112.176760093132 \wedge x \leq -110.176760093132$$
$$x \geq -108.176760093132 \wedge x \leq -106.176760093132$$
$$x \geq -104.176760093132 \wedge x \leq -102.176760093132$$
$$x \geq -100.176760093132 \wedge x \leq -98.176760093132$$
$$x \geq -96.176760093132 \wedge x \leq -94.176760093132$$
$$x \geq -92.176760093132 \wedge x \leq -90.176760093132$$
$$x \geq -88.176760093132 \wedge x \leq -86.176760093132$$
$$x \geq -84.176760093132 \wedge x \leq -82.176760093132$$
$$x \geq -80.176760093132 \wedge x \leq -78.176760093132$$
$$x \geq -76.1767600931321 \wedge x \leq -74.1767600931323$$
$$x \geq -72.1767600931332 \wedge x \leq -70.1767600931369$$
$$x \geq -68.1767600931515 \wedge x \leq -66.1767600932097$$
$$x \geq -64.1767600934429 \wedge x \leq -62.1767600943758$$
$$x \geq -60.1767600981082 \wedge x \leq -58.1767601130444$$
$$x \geq -56.1767601728291 \wedge x \leq -54.1767604122184$$
$$x \geq -52.1767613713416 \wedge x \leq -50.176765217626$$
$$x \geq -48.1767806640327 \wedge x \leq -46.1768428337543$$
$$x \geq -44.1770939320033 \wedge x \leq 0$$
$$x \geq 3$$
Solución de la desigualdad en el gráfico
Gráfico