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:
-
4+12x>7+13x
-
x-4x^2/x-1>0
-
1/4x>1
-
x+2<5x-2(x-3)
- Gráfico de la función y =:
- |sinx+1|
-
Expresiones idénticas
- |sinx+ uno |> uno , cinco ,
- módulo de seno de x más 1| más 1,5,
- módulo de seno de x más uno | más uno , cinco ,
-
Expresiones semejantes
- |sinx-1|>1,5,
-
Expresiones con funciones
- sinx
- sinx<=(sqrt(3)/2)
- sinx>=-sqrt(2)
- sinx+sin2x+sin3x>0
- sinx+sin(x/2)>0
- sinx<=cos^2x
- Módulo |
- |x+3|<7
- |x-2|<5
- |x^2+6x|<=0
- |x^2+x+1|<=|x^2+3x+4|
- |x/3+1|>2
|sinx+1|>1,5, desigualdades
Solución
Ha introducido
[src]
|sin(x) + 1| > 3/2
$$\left|{\sin{\left(x \right)} + 1}\right| > \frac{3}{2}$$
Abs(sin(x) + 1) > 3/2
Solución detallada
Se da la desigualdad:
$$\left|{\sin{\left(x \right)} + 1}\right| > \frac{3}{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left|{\sin{\left(x \right)} + 1}\right| = \frac{3}{2}$$
Resolvemos:
$$x_{1} = 71.733032256967$$
$$x_{2} = 78.0162175641465$$
$$x_{3} = -81.1578102177363$$
$$x_{4} = 69.6386371545737$$
$$x_{5} = 25.6563400043166$$
$$x_{6} = -79.0634151153431$$
$$x_{7} = -12.0427718387609$$
$$x_{8} = 82.2050077689329$$
$$x_{9} = -60.2138591938044$$
$$x_{10} = 101.054563690472$$
$$x_{11} = -24.60914245312$$
$$x_{12} = 138.753675533549$$
$$x_{13} = -53.9306738866248$$
$$x_{14} = -97.9129710368819$$
$$x_{15} = -72.7802298081635$$
$$x_{16} = -18.3259571459405$$
$$x_{17} = -43.4586983746588$$
$$x_{18} = 90.5825881785057$$
$$x_{19} = 6.80678408277789$$
$$x_{20} = 17438.4572213013$$
$$x_{21} = 84.2994028713261$$
$$x_{22} = 59.1666616426078$$
$$x_{23} = 63.3554518473942$$
$$x_{24} = 0.523598775598299$$
$$x_{25} = -56.025068989018$$
$$x_{26} = -16.2315620435473$$
$$x_{27} = 38.2227106186758$$
$$x_{28} = -22.5147473507269$$
$$x_{29} = 31.9395253114962$$
$$x_{30} = -37.1755130674792$$
$$x_{31} = 134.564885328763$$
$$x_{32} = -30.8923277602996$$
$$x_{33} = 40.317105721069$$
$$x_{34} = 88.4881930761125$$
$$x_{35} = 50.789081233035$$
$$x_{36} = 13.0899693899575$$
$$x_{37} = -62.3082542961976$$
$$x_{38} = -28.7979326579064$$
$$x_{39} = -41.3643032722656$$
$$x_{40} = -74.8746249105567$$
$$x_{41} = 44.5058959258554$$
$$x_{42} = -85.3466004225227$$
$$x_{43} = -47.6474885794452$$
$$x_{44} = 94.7713783832921$$
$$x_{45} = -9.94837673636768$$
$$x_{46} = -91.6297857297023$$
$$x_{47} = 46.6002910282486$$
$$x_{48} = -3.66519142918809$$
$$x_{49} = 75.9218224617533$$
$$x_{50} = 96.8657734856853$$
$$x_{51} = 34.0339204138894$$
$$x_{52} = -5.75958653158129$$
$$x_{53} = -100.007366139275$$
$$x_{54} = -66.497044500984$$
$$x_{55} = -2650.98060085419$$
$$x_{56} = -627.79493194236$$
$$x_{57} = -49.7418836818384$$
$$x_{58} = -35.081117965086$$
$$x_{59} = 52.8834763354282$$
$$x_{60} = 2.61799387799149$$
$$x_{61} = 19.3731546971371$$
$$x_{62} = -87.4409955249159$$
$$x_{63} = 65.4498469497874$$
$$x_{64} = 8.90117918517108$$
$$x_{65} = 21.4675497995303$$
$$x_{66} = 57.0722665402146$$
$$x_{67} = -93.7241808320955$$
$$x_{68} = -4454.25478401473$$
$$x_{69} = 27.7507351067098$$
$$x_{70} = 15.1843644923507$$
$$x_{71} = -68.5914396033772$$
$$x_{1} = 71.733032256967$$
$$x_{2} = 78.0162175641465$$
$$x_{3} = -81.1578102177363$$
$$x_{4} = 69.6386371545737$$
$$x_{5} = 25.6563400043166$$
$$x_{6} = -79.0634151153431$$
$$x_{7} = -12.0427718387609$$
$$x_{8} = 82.2050077689329$$
$$x_{9} = -60.2138591938044$$
$$x_{10} = 101.054563690472$$
$$x_{11} = -24.60914245312$$
$$x_{12} = 138.753675533549$$
$$x_{13} = -53.9306738866248$$
$$x_{14} = -97.9129710368819$$
$$x_{15} = -72.7802298081635$$
$$x_{16} = -18.3259571459405$$
$$x_{17} = -43.4586983746588$$
$$x_{18} = 90.5825881785057$$
$$x_{19} = 6.80678408277789$$
$$x_{20} = 17438.4572213013$$
$$x_{21} = 84.2994028713261$$
$$x_{22} = 59.1666616426078$$
$$x_{23} = 63.3554518473942$$
$$x_{24} = 0.523598775598299$$
$$x_{25} = -56.025068989018$$
$$x_{26} = -16.2315620435473$$
$$x_{27} = 38.2227106186758$$
$$x_{28} = -22.5147473507269$$
$$x_{29} = 31.9395253114962$$
$$x_{30} = -37.1755130674792$$
$$x_{31} = 134.564885328763$$
$$x_{32} = -30.8923277602996$$
$$x_{33} = 40.317105721069$$
$$x_{34} = 88.4881930761125$$
$$x_{35} = 50.789081233035$$
$$x_{36} = 13.0899693899575$$
$$x_{37} = -62.3082542961976$$
$$x_{38} = -28.7979326579064$$
$$x_{39} = -41.3643032722656$$
$$x_{40} = -74.8746249105567$$
$$x_{41} = 44.5058959258554$$
$$x_{42} = -85.3466004225227$$
$$x_{43} = -47.6474885794452$$
$$x_{44} = 94.7713783832921$$
$$x_{45} = -9.94837673636768$$
$$x_{46} = -91.6297857297023$$
$$x_{47} = 46.6002910282486$$
$$x_{48} = -3.66519142918809$$
$$x_{49} = 75.9218224617533$$
$$x_{50} = 96.8657734856853$$
$$x_{51} = 34.0339204138894$$
$$x_{52} = -5.75958653158129$$
$$x_{53} = -100.007366139275$$
$$x_{54} = -66.497044500984$$
$$x_{55} = -2650.98060085419$$
$$x_{56} = -627.79493194236$$
$$x_{57} = -49.7418836818384$$
$$x_{58} = -35.081117965086$$
$$x_{59} = 52.8834763354282$$
$$x_{60} = 2.61799387799149$$
$$x_{61} = 19.3731546971371$$
$$x_{62} = -87.4409955249159$$
$$x_{63} = 65.4498469497874$$
$$x_{64} = 8.90117918517108$$
$$x_{65} = 21.4675497995303$$
$$x_{66} = 57.0722665402146$$
$$x_{67} = -93.7241808320955$$
$$x_{68} = -4454.25478401473$$
$$x_{69} = 27.7507351067098$$
$$x_{70} = 15.1843644923507$$
$$x_{71} = -68.5914396033772$$
Las raíces dadas
$$x_{68} = -4454.25478401473$$
$$x_{55} = -2650.98060085419$$
$$x_{56} = -627.79493194236$$
$$x_{53} = -100.007366139275$$
$$x_{14} = -97.9129710368819$$
$$x_{67} = -93.7241808320955$$
$$x_{46} = -91.6297857297023$$
$$x_{62} = -87.4409955249159$$
$$x_{42} = -85.3466004225227$$
$$x_{3} = -81.1578102177363$$
$$x_{6} = -79.0634151153431$$
$$x_{40} = -74.8746249105567$$
$$x_{15} = -72.7802298081635$$
$$x_{71} = -68.5914396033772$$
$$x_{54} = -66.497044500984$$
$$x_{37} = -62.3082542961976$$
$$x_{9} = -60.2138591938044$$
$$x_{25} = -56.025068989018$$
$$x_{13} = -53.9306738866248$$
$$x_{57} = -49.7418836818384$$
$$x_{43} = -47.6474885794452$$
$$x_{17} = -43.4586983746588$$
$$x_{39} = -41.3643032722656$$
$$x_{30} = -37.1755130674792$$
$$x_{58} = -35.081117965086$$
$$x_{32} = -30.8923277602996$$
$$x_{38} = -28.7979326579064$$
$$x_{11} = -24.60914245312$$
$$x_{28} = -22.5147473507269$$
$$x_{16} = -18.3259571459405$$
$$x_{26} = -16.2315620435473$$
$$x_{7} = -12.0427718387609$$
$$x_{45} = -9.94837673636768$$
$$x_{52} = -5.75958653158129$$
$$x_{48} = -3.66519142918809$$
$$x_{24} = 0.523598775598299$$
$$x_{60} = 2.61799387799149$$
$$x_{19} = 6.80678408277789$$
$$x_{64} = 8.90117918517108$$
$$x_{36} = 13.0899693899575$$
$$x_{70} = 15.1843644923507$$
$$x_{61} = 19.3731546971371$$
$$x_{65} = 21.4675497995303$$
$$x_{5} = 25.6563400043166$$
$$x_{69} = 27.7507351067098$$
$$x_{29} = 31.9395253114962$$
$$x_{51} = 34.0339204138894$$
$$x_{27} = 38.2227106186758$$
$$x_{33} = 40.317105721069$$
$$x_{41} = 44.5058959258554$$
$$x_{47} = 46.6002910282486$$
$$x_{35} = 50.789081233035$$
$$x_{59} = 52.8834763354282$$
$$x_{66} = 57.0722665402146$$
$$x_{22} = 59.1666616426078$$
$$x_{23} = 63.3554518473942$$
$$x_{63} = 65.4498469497874$$
$$x_{4} = 69.6386371545737$$
$$x_{1} = 71.733032256967$$
$$x_{49} = 75.9218224617533$$
$$x_{2} = 78.0162175641465$$
$$x_{8} = 82.2050077689329$$
$$x_{21} = 84.2994028713261$$
$$x_{34} = 88.4881930761125$$
$$x_{18} = 90.5825881785057$$
$$x_{44} = 94.7713783832921$$
$$x_{50} = 96.8657734856853$$
$$x_{10} = 101.054563690472$$
$$x_{31} = 134.564885328763$$
$$x_{12} = 138.753675533549$$
$$x_{20} = 17438.4572213013$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{68}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{68} - \frac{1}{10}$$
=
$$-4454.25478401473 + - \frac{1}{10}$$
=
$$-4454.35478401473$$
lo sustituimos en la expresión
$$\left|{\sin{\left(x \right)} + 1}\right| > \frac{3}{2}$$
$$\left|{\sin{\left(-4454.35478401473 \right)} + 1}\right| > \frac{3}{2}$$
Entonces
$$x < -4454.25478401473$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -4454.25478401473 \wedge x < -2650.98060085419$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -4454.25478401473 \wedge x < -2650.98060085419$$
$$x > -627.79493194236 \wedge x < -100.007366139275$$
$$x > -97.9129710368819 \wedge x < -93.7241808320955$$
$$x > -91.6297857297023 \wedge x < -87.4409955249159$$
$$x > -85.3466004225227 \wedge x < -81.1578102177363$$
$$x > -79.0634151153431 \wedge x < -74.8746249105567$$
$$x > -72.7802298081635 \wedge x < -68.5914396033772$$
$$x > -66.497044500984 \wedge x < -62.3082542961976$$
$$x > -60.2138591938044 \wedge x < -56.025068989018$$
$$x > -53.9306738866248 \wedge x < -49.7418836818384$$
$$x > -47.6474885794452 \wedge x < -43.4586983746588$$
$$x > -41.3643032722656 \wedge x < -37.1755130674792$$
$$x > -35.081117965086 \wedge x < -30.8923277602996$$
$$x > -28.7979326579064 \wedge x < -24.60914245312$$
$$x > -22.5147473507269 \wedge x < -18.3259571459405$$
$$x > -16.2315620435473 \wedge x < -12.0427718387609$$
$$x > -9.94837673636768 \wedge x < -5.75958653158129$$
$$x > -3.66519142918809 \wedge x < 0.523598775598299$$
$$x > 2.61799387799149 \wedge x < 6.80678408277789$$
$$x > 8.90117918517108 \wedge x < 13.0899693899575$$
$$x > 15.1843644923507 \wedge x < 19.3731546971371$$
$$x > 21.4675497995303 \wedge x < 25.6563400043166$$
$$x > 27.7507351067098 \wedge x < 31.9395253114962$$
$$x > 34.0339204138894 \wedge x < 38.2227106186758$$
$$x > 40.317105721069 \wedge x < 44.5058959258554$$
$$x > 46.6002910282486 \wedge x < 50.789081233035$$
$$x > 52.8834763354282 \wedge x < 57.0722665402146$$
$$x > 59.1666616426078 \wedge x < 63.3554518473942$$
$$x > 65.4498469497874 \wedge x < 69.6386371545737$$
$$x > 71.733032256967 \wedge x < 75.9218224617533$$
$$x > 78.0162175641465 \wedge x < 82.2050077689329$$
$$x > 84.2994028713261 \wedge x < 88.4881930761125$$
$$x > 90.5825881785057 \wedge x < 94.7713783832921$$
$$x > 96.8657734856853 \wedge x < 101.054563690472$$
$$x > 134.564885328763 \wedge x < 138.753675533549$$
$$x > 17438.4572213013$$
$$\left|{\sin{\left(x \right)} + 1}\right| > \frac{3}{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left|{\sin{\left(x \right)} + 1}\right| = \frac{3}{2}$$
Resolvemos:
$$x_{1} = 71.733032256967$$
$$x_{2} = 78.0162175641465$$
$$x_{3} = -81.1578102177363$$
$$x_{4} = 69.6386371545737$$
$$x_{5} = 25.6563400043166$$
$$x_{6} = -79.0634151153431$$
$$x_{7} = -12.0427718387609$$
$$x_{8} = 82.2050077689329$$
$$x_{9} = -60.2138591938044$$
$$x_{10} = 101.054563690472$$
$$x_{11} = -24.60914245312$$
$$x_{12} = 138.753675533549$$
$$x_{13} = -53.9306738866248$$
$$x_{14} = -97.9129710368819$$
$$x_{15} = -72.7802298081635$$
$$x_{16} = -18.3259571459405$$
$$x_{17} = -43.4586983746588$$
$$x_{18} = 90.5825881785057$$
$$x_{19} = 6.80678408277789$$
$$x_{20} = 17438.4572213013$$
$$x_{21} = 84.2994028713261$$
$$x_{22} = 59.1666616426078$$
$$x_{23} = 63.3554518473942$$
$$x_{24} = 0.523598775598299$$
$$x_{25} = -56.025068989018$$
$$x_{26} = -16.2315620435473$$
$$x_{27} = 38.2227106186758$$
$$x_{28} = -22.5147473507269$$
$$x_{29} = 31.9395253114962$$
$$x_{30} = -37.1755130674792$$
$$x_{31} = 134.564885328763$$
$$x_{32} = -30.8923277602996$$
$$x_{33} = 40.317105721069$$
$$x_{34} = 88.4881930761125$$
$$x_{35} = 50.789081233035$$
$$x_{36} = 13.0899693899575$$
$$x_{37} = -62.3082542961976$$
$$x_{38} = -28.7979326579064$$
$$x_{39} = -41.3643032722656$$
$$x_{40} = -74.8746249105567$$
$$x_{41} = 44.5058959258554$$
$$x_{42} = -85.3466004225227$$
$$x_{43} = -47.6474885794452$$
$$x_{44} = 94.7713783832921$$
$$x_{45} = -9.94837673636768$$
$$x_{46} = -91.6297857297023$$
$$x_{47} = 46.6002910282486$$
$$x_{48} = -3.66519142918809$$
$$x_{49} = 75.9218224617533$$
$$x_{50} = 96.8657734856853$$
$$x_{51} = 34.0339204138894$$
$$x_{52} = -5.75958653158129$$
$$x_{53} = -100.007366139275$$
$$x_{54} = -66.497044500984$$
$$x_{55} = -2650.98060085419$$
$$x_{56} = -627.79493194236$$
$$x_{57} = -49.7418836818384$$
$$x_{58} = -35.081117965086$$
$$x_{59} = 52.8834763354282$$
$$x_{60} = 2.61799387799149$$
$$x_{61} = 19.3731546971371$$
$$x_{62} = -87.4409955249159$$
$$x_{63} = 65.4498469497874$$
$$x_{64} = 8.90117918517108$$
$$x_{65} = 21.4675497995303$$
$$x_{66} = 57.0722665402146$$
$$x_{67} = -93.7241808320955$$
$$x_{68} = -4454.25478401473$$
$$x_{69} = 27.7507351067098$$
$$x_{70} = 15.1843644923507$$
$$x_{71} = -68.5914396033772$$
$$x_{1} = 71.733032256967$$
$$x_{2} = 78.0162175641465$$
$$x_{3} = -81.1578102177363$$
$$x_{4} = 69.6386371545737$$
$$x_{5} = 25.6563400043166$$
$$x_{6} = -79.0634151153431$$
$$x_{7} = -12.0427718387609$$
$$x_{8} = 82.2050077689329$$
$$x_{9} = -60.2138591938044$$
$$x_{10} = 101.054563690472$$
$$x_{11} = -24.60914245312$$
$$x_{12} = 138.753675533549$$
$$x_{13} = -53.9306738866248$$
$$x_{14} = -97.9129710368819$$
$$x_{15} = -72.7802298081635$$
$$x_{16} = -18.3259571459405$$
$$x_{17} = -43.4586983746588$$
$$x_{18} = 90.5825881785057$$
$$x_{19} = 6.80678408277789$$
$$x_{20} = 17438.4572213013$$
$$x_{21} = 84.2994028713261$$
$$x_{22} = 59.1666616426078$$
$$x_{23} = 63.3554518473942$$
$$x_{24} = 0.523598775598299$$
$$x_{25} = -56.025068989018$$
$$x_{26} = -16.2315620435473$$
$$x_{27} = 38.2227106186758$$
$$x_{28} = -22.5147473507269$$
$$x_{29} = 31.9395253114962$$
$$x_{30} = -37.1755130674792$$
$$x_{31} = 134.564885328763$$
$$x_{32} = -30.8923277602996$$
$$x_{33} = 40.317105721069$$
$$x_{34} = 88.4881930761125$$
$$x_{35} = 50.789081233035$$
$$x_{36} = 13.0899693899575$$
$$x_{37} = -62.3082542961976$$
$$x_{38} = -28.7979326579064$$
$$x_{39} = -41.3643032722656$$
$$x_{40} = -74.8746249105567$$
$$x_{41} = 44.5058959258554$$
$$x_{42} = -85.3466004225227$$
$$x_{43} = -47.6474885794452$$
$$x_{44} = 94.7713783832921$$
$$x_{45} = -9.94837673636768$$
$$x_{46} = -91.6297857297023$$
$$x_{47} = 46.6002910282486$$
$$x_{48} = -3.66519142918809$$
$$x_{49} = 75.9218224617533$$
$$x_{50} = 96.8657734856853$$
$$x_{51} = 34.0339204138894$$
$$x_{52} = -5.75958653158129$$
$$x_{53} = -100.007366139275$$
$$x_{54} = -66.497044500984$$
$$x_{55} = -2650.98060085419$$
$$x_{56} = -627.79493194236$$
$$x_{57} = -49.7418836818384$$
$$x_{58} = -35.081117965086$$
$$x_{59} = 52.8834763354282$$
$$x_{60} = 2.61799387799149$$
$$x_{61} = 19.3731546971371$$
$$x_{62} = -87.4409955249159$$
$$x_{63} = 65.4498469497874$$
$$x_{64} = 8.90117918517108$$
$$x_{65} = 21.4675497995303$$
$$x_{66} = 57.0722665402146$$
$$x_{67} = -93.7241808320955$$
$$x_{68} = -4454.25478401473$$
$$x_{69} = 27.7507351067098$$
$$x_{70} = 15.1843644923507$$
$$x_{71} = -68.5914396033772$$
Las raíces dadas
$$x_{68} = -4454.25478401473$$
$$x_{55} = -2650.98060085419$$
$$x_{56} = -627.79493194236$$
$$x_{53} = -100.007366139275$$
$$x_{14} = -97.9129710368819$$
$$x_{67} = -93.7241808320955$$
$$x_{46} = -91.6297857297023$$
$$x_{62} = -87.4409955249159$$
$$x_{42} = -85.3466004225227$$
$$x_{3} = -81.1578102177363$$
$$x_{6} = -79.0634151153431$$
$$x_{40} = -74.8746249105567$$
$$x_{15} = -72.7802298081635$$
$$x_{71} = -68.5914396033772$$
$$x_{54} = -66.497044500984$$
$$x_{37} = -62.3082542961976$$
$$x_{9} = -60.2138591938044$$
$$x_{25} = -56.025068989018$$
$$x_{13} = -53.9306738866248$$
$$x_{57} = -49.7418836818384$$
$$x_{43} = -47.6474885794452$$
$$x_{17} = -43.4586983746588$$
$$x_{39} = -41.3643032722656$$
$$x_{30} = -37.1755130674792$$
$$x_{58} = -35.081117965086$$
$$x_{32} = -30.8923277602996$$
$$x_{38} = -28.7979326579064$$
$$x_{11} = -24.60914245312$$
$$x_{28} = -22.5147473507269$$
$$x_{16} = -18.3259571459405$$
$$x_{26} = -16.2315620435473$$
$$x_{7} = -12.0427718387609$$
$$x_{45} = -9.94837673636768$$
$$x_{52} = -5.75958653158129$$
$$x_{48} = -3.66519142918809$$
$$x_{24} = 0.523598775598299$$
$$x_{60} = 2.61799387799149$$
$$x_{19} = 6.80678408277789$$
$$x_{64} = 8.90117918517108$$
$$x_{36} = 13.0899693899575$$
$$x_{70} = 15.1843644923507$$
$$x_{61} = 19.3731546971371$$
$$x_{65} = 21.4675497995303$$
$$x_{5} = 25.6563400043166$$
$$x_{69} = 27.7507351067098$$
$$x_{29} = 31.9395253114962$$
$$x_{51} = 34.0339204138894$$
$$x_{27} = 38.2227106186758$$
$$x_{33} = 40.317105721069$$
$$x_{41} = 44.5058959258554$$
$$x_{47} = 46.6002910282486$$
$$x_{35} = 50.789081233035$$
$$x_{59} = 52.8834763354282$$
$$x_{66} = 57.0722665402146$$
$$x_{22} = 59.1666616426078$$
$$x_{23} = 63.3554518473942$$
$$x_{63} = 65.4498469497874$$
$$x_{4} = 69.6386371545737$$
$$x_{1} = 71.733032256967$$
$$x_{49} = 75.9218224617533$$
$$x_{2} = 78.0162175641465$$
$$x_{8} = 82.2050077689329$$
$$x_{21} = 84.2994028713261$$
$$x_{34} = 88.4881930761125$$
$$x_{18} = 90.5825881785057$$
$$x_{44} = 94.7713783832921$$
$$x_{50} = 96.8657734856853$$
$$x_{10} = 101.054563690472$$
$$x_{31} = 134.564885328763$$
$$x_{12} = 138.753675533549$$
$$x_{20} = 17438.4572213013$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{68}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{68} - \frac{1}{10}$$
=
$$-4454.25478401473 + - \frac{1}{10}$$
=
$$-4454.35478401473$$
lo sustituimos en la expresión
$$\left|{\sin{\left(x \right)} + 1}\right| > \frac{3}{2}$$
$$\left|{\sin{\left(-4454.35478401473 \right)} + 1}\right| > \frac{3}{2}$$
1.41104380767631 > 3/2
Entonces
$$x < -4454.25478401473$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -4454.25478401473 \wedge x < -2650.98060085419$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------
x68 x55 x56 x53 x14 x67 x46 x62 x42 x3 x6 x40 x15 x71 x54 x37 x9 x25 x13 x57 x43 x17 x39 x30 x58 x32 x38 x11 x28 x16 x26 x7 x45 x52 x48 x24 x60 x19 x64 x36 x70 x61 x65 x5 x69 x29 x51 x27 x33 x41 x47 x35 x59 x66 x22 x23 x63 x4 x1 x49 x2 x8 x21 x34 x18 x44 x50 x10 x31 x12 x20Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -4454.25478401473 \wedge x < -2650.98060085419$$
$$x > -627.79493194236 \wedge x < -100.007366139275$$
$$x > -97.9129710368819 \wedge x < -93.7241808320955$$
$$x > -91.6297857297023 \wedge x < -87.4409955249159$$
$$x > -85.3466004225227 \wedge x < -81.1578102177363$$
$$x > -79.0634151153431 \wedge x < -74.8746249105567$$
$$x > -72.7802298081635 \wedge x < -68.5914396033772$$
$$x > -66.497044500984 \wedge x < -62.3082542961976$$
$$x > -60.2138591938044 \wedge x < -56.025068989018$$
$$x > -53.9306738866248 \wedge x < -49.7418836818384$$
$$x > -47.6474885794452 \wedge x < -43.4586983746588$$
$$x > -41.3643032722656 \wedge x < -37.1755130674792$$
$$x > -35.081117965086 \wedge x < -30.8923277602996$$
$$x > -28.7979326579064 \wedge x < -24.60914245312$$
$$x > -22.5147473507269 \wedge x < -18.3259571459405$$
$$x > -16.2315620435473 \wedge x < -12.0427718387609$$
$$x > -9.94837673636768 \wedge x < -5.75958653158129$$
$$x > -3.66519142918809 \wedge x < 0.523598775598299$$
$$x > 2.61799387799149 \wedge x < 6.80678408277789$$
$$x > 8.90117918517108 \wedge x < 13.0899693899575$$
$$x > 15.1843644923507 \wedge x < 19.3731546971371$$
$$x > 21.4675497995303 \wedge x < 25.6563400043166$$
$$x > 27.7507351067098 \wedge x < 31.9395253114962$$
$$x > 34.0339204138894 \wedge x < 38.2227106186758$$
$$x > 40.317105721069 \wedge x < 44.5058959258554$$
$$x > 46.6002910282486 \wedge x < 50.789081233035$$
$$x > 52.8834763354282 \wedge x < 57.0722665402146$$
$$x > 59.1666616426078 \wedge x < 63.3554518473942$$
$$x > 65.4498469497874 \wedge x < 69.6386371545737$$
$$x > 71.733032256967 \wedge x < 75.9218224617533$$
$$x > 78.0162175641465 \wedge x < 82.2050077689329$$
$$x > 84.2994028713261 \wedge x < 88.4881930761125$$
$$x > 90.5825881785057 \wedge x < 94.7713783832921$$
$$x > 96.8657734856853 \wedge x < 101.054563690472$$
$$x > 134.564885328763 \wedge x < 138.753675533549$$
$$x > 17438.4572213013$$
Solución de la desigualdad en el gráfico