 Resolucion de Guia de Inecuaciones |
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Foro fmat.cl > Programa Enseñanza Universitaria > Comunidades Universitarias > Universidad de Santiago de Chile > Cálculo  |
 May 18 2008, 11:27 AM
Publicado:
#1
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Dios Matemático Supremo Grupo: Baneado Mensajes: 1.737 Registrado: 6-September 07 Miembro Nº: 9.900  |
A pedido de Krizalid, Resolvamos Uno por uno los ejercicios de esta guía. guía de Inecuaciones
![TEX: <br />1) % MathType!MTEF!2!1!+-<br />% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn<br />% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr<br />% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9<br />% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x<br />% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaadaWcaa<br />% qaaiaaigdaaeaacaaI0aaaamaabmaabaGaaGOmaiaadIhacqGHsisl<br />% caaIXaaacaGLOaGaayzkaaGaeyOeI0IaamiEaiabgYda8maalaaaba<br />% GaamiEaaqaaiaaiAdaaaGaeyOeI0YaaSaaaeaacaaIXaaabaGaaG4m<br />% aaaacaaMb8UaaGzaVlaaykW7caaMc8UaaGPaVlaac+cacaGGOaGaaG<br />% PaVlaacMcacqGHflY1caaMc8UaaGymaiaaikdaaeaaaeaacaaIZaGa<br />% aiikaiaaikdacaWG4bGaeyOeI0IaaGymaiaacMcacqGHsislcaaIXa<br />% GaaGOmaiaadIhacqGH8aapcaaIYaGaamiEaiabgkHiTia.aisdaaeaa<br />% caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaI2aGaamiEai<br />% abgkHiTiaaiodacqGHsislcaaIXaGaaGOmaiaadIhacqGH8aapcaaI<br />% YaGaamiEaiabgkHiTiaaisdaaeaacaaMc8UaaGPaVlaaykW7caaMc8<br />% UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7<br />% caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVl<br />% aaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8Ua<br />% aGPaVlaaykW7caaIXaGaaGPaVlabgYda8iaaiIdacaWG4baabaGaaG<br />% PaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaM<br />% c8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaayk<br />% W7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPa<br />% VlaaykW7caaMc8UaaGPaVlaaykW7caaMc8+aaSaaaeaacaaIXaaaba<br />% GaaGioaaaacqGH8aapcaWG4baaaaa!DB10!<br />\[<br />\begin{gathered}<br /> \frac{1}<br />{4}\left( {2x - 1} \right) - x < \frac{x}<br />{6} - \frac{1}<br />{3}\,\,\,/(\,) \cdot \,12 \hfill \\<br /> \hfill \\<br /> 3(2x - 1) - 12x < 2x - 4 \hfill \\<br /> \,\,\,\,\,\,6x - 3 - 12x < 2x - 4 \hfill \\<br /> \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1\, < 8x \hfill \\<br /> \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{1}<br />{8} < x \hfill \\ <br />\end{gathered} <br />\]<br /><br />](./tex/6ee7a8dc3992f3eed9971ed33b0c7703.png) . Psdt. Jajja, Igual terrible metío, si yo soy de la federico...jaja Mensaje modificado por deixo el May 18 2008, 12:25 PM |
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May 18 2008, 11:46 AM
Publicado:
#2
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Dios Matemático Supremo Grupo: Baneado Mensajes: 1.737 Registrado: 6-September 07 Miembro Nº: 9.900 |
![TEX: % MathType!MTEF!2!1!+-<br />% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn<br />% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr<br />% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9<br />% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x<br />% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaaIYa<br />% GaaiykaaqaaiaaikdacaWG4bGaey4kaSIaaGymaiabgYda8iaaioda<br />% cqGHsislcaWG4bGaeyipaWJaaGOmaiaadIhacqGHRaWkcaaI1aGaaG<br />% PaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaM<br />% c8Uaai4laiabgkHiTiaaiodaaeaacaaMc8UaaGPaVlaaykW7caaMc8<br />% UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaIXaGaeyipaWJaaG4m<br />% aiabgkHiTiaaiodacaWG4bGaeyipaWJaaGynaiaaykW7caaMc8UaaG<br />% PaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaM<br />% c8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8Uaai4laiabgw<br />% SixlabgkHiTiaaigdaaeaacqGHsislcaaIXaGaeyOpa4JaaG4maiaa<br />% dIhacqGHsislcaaIZaGaeyOpa4JaeyOeI0IaaGynaiaaykW7caaMc8<br />% UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7<br />% caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVl<br />% aaykW7caGGVaGaey4kaSIaaG4maaqaaiaaykW7caaMc8UaaGPaVlaa<br />% ykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaIYaGaey<br />% Opa4JaaG4maiaadIhacqGH+aGpcqGHsislcaaIYaGaaGPaVlaaykW7<br />% caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVl<br />% aaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8Ua<br />% ai4laiabgEpa4kaaiodaaeaacaaMc8UaaGPaVlaaykW7caaMc8UaaG<br />% PaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVpaaL4babaWa<br />% aSaaaeaacaaIYaaabaGaaG4maaaacqGH+aGpcaWG4bGaeyOpa4ZaaS<br />% aaaeaacqGHsislcaaIYaaabaGaaG4maaaaaaaaaaa!FC6E!<br />\[<br />\begin{gathered}<br /> 2) \hfill \\<br /> 2x + 1 < 3 - x < 2x + 5\,\,\,\,\,\,\,\,\,/ - 3 \hfill \\<br /> \,\,\,\,\,\,\,\,\,1 < 3 - 3x < 5\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,/ \cdot - 1 \hfill \\<br /> - 1 > 3x - 3 > - 5\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,/ + 3 \hfill \\<br /> \,\,\,\,\,\,\,\,\,\,2 > 3x > - 2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,/ \div 3 \hfill \\<br /> \,\,\,\,\,\,\,\,\,\,\,\boxed{\frac{2}<br />{3} > x > \frac{{ - 2}}<br />{3}} \hfill \\ <br />\end{gathered} <br />\]<br />](./tex/fc90334d99210ef2c98512c2c3cb8252.png)
Mensaje modificado por deixo el May 18 2008, 11:47 AM |
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May 18 2008, 12:02 PM
Publicado:
#3
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Dios Matemático Supremo Grupo: Baneado Mensajes: 1.737 Registrado: 6-September 07 Miembro Nº: 9.900 |
![TEX: % MathType!MTEF!2!1!+-<br />% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn<br />% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr<br />% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9<br />% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x<br />% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaaIZa<br />% GaaiykaaqaaaqaaiaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPa<br />% VlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8<br />% UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7<br />% caaMc8UaaG4maiaadIhacqGHRaWkcaaI3aGaeyOpa4JaaGynaiabgk<br />% HiTiaaikdacaWG4bGaeyyzImRaaGymaiaaiodacqGHsislcaaI2aGa<br />% amiEaaqaaaqaaiaaykW7caaMc8UaaGPaVlaadMgacaGGPaGaaG4mai<br />% aadIhacqGHRaWkcaaI3aGaeyOpa4JaaGynaiabgkHiTiaaikdacaWG<br />% 4bGaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaayk<br />% W7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPa<br />% VlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caWGPb<br />% GaamyAaiaacMcacaaMc8UaaGPaVlaaiwdacqGHsislcaaIYaGaamiE<br />% aiabgwMiZkaaigdacaaIZaGaeyOeI0IaaGOnaiaadIhaaeaacaaMc8<br />% UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7<br />% caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaiwdacaWG4bGaeyOpa4<br />% JaeyOeI0IaaGOmaiaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPa<br />% VlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8<br />% UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7<br />% caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVl<br />% aaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaisdacaWG4bGa<br />% eyyzImRaaGioaiaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVl<br />% aaykW7caaMc8oabaGaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaM<br />% c8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaayk<br />% W7caaMc8UaaGPaVpaaL4babaGaamiEaiabg6da+maalaaabaGaeyOe<br />% I0IaaGOmaaqaaiaaiwdaaaaaaiaaykW7caaMc8UaaGPaVlaaykW7ca<br />% aMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaa<br />% ykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaG<br />% PaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaM<br />% c8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7daqjEaqaaiaadIhacq<br />% GHLjYScaaIYaGaaGPaVdaaaaaa!626A!<br />\[<br />\begin{gathered}<br /> 3) \hfill \\<br /> \hfill \\<br /> \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3x + 7 > 5 - 2x \geqslant 13 - 6x \hfill \\<br /> \hfill \\<br /> \,\,\,i)3x + 7 > 5 - 2x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,ii)\,\,5 - 2x \geqslant 13 - 6x \hfill \\<br /> \,\,\,\,\,\,\,\,\,\,\,\,\,\,5x > - 2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4x \geqslant 8\,\,\,\,\,\,\,\, \hfill \\<br /> \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\boxed{x > \frac{{ - 2}}<br />{5}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\boxed{x \geqslant 2\,} \hfill \\ <br />\end{gathered} <br />\]<br />](./tex/66e99638ea62384e234bb751bee0d400.png)
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May 18 2008, 12:07 PM
Publicado:
#4
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Dios Matemático Supremo Grupo: Baneado Mensajes: 1.737 Registrado: 6-September 07 Miembro Nº: 9.900 |
![TEX: % MathType!MTEF!2!1!+-<br />% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn<br />% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr<br />% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9<br />% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x<br />% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaaI0a<br />% GaaiykaaqaaaqaaiaaiodacaWG4bGaeyOeI0IaaGynaiabgsMiJkaa<br />% igdacqGHRaWkcaWG4bGaeyizImQaaGOmaiaadIhacqGHsislcaaIZa<br />% aabaaabaGaamyAaiaacMcacaaMc8UaaGPaVlaaiodacaWG4bGaeyOe<br />% I0IaaGynaiabgsMiJkaaigdacqGHRaWkcaWG4baabaGaaGPaVlaayk<br />% W7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPa<br />% VlaaykW7caaMc8UaaGOmaiaadIhacqGHKjYOcaaI2aaabaGaaGPaVl<br />% aaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8Ua<br />% aGPaVlaaykW7caaMc8UaaGPaVpaaL4babaGaaGPaVlaadIhacqGHKj<br />% YOcaaIZaaaaaqaaaqaaiaadMgacaGGPaGaaGPaVlaaykW7caaMc8Ua<br />% aGymaiabgUcaRiaadIhacqGHKjYOcaaIYaGaamiEaiabgkHiTiaaio<br />% daaeaacaaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8Ua<br />% aGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8+aauIhaeaacaaI0a<br />% GaeyizImQaamiEaaaaaaaa!A650!<br />\[<br />\begin{gathered}<br /> 4) \hfill \\<br /> \hfill \\<br /> 3x - 5 \leqslant 1 + x \leqslant 2x - 3 \hfill \\<br /> \hfill \\<br /> i)\,\,3x - 5 \leqslant 1 + x \hfill \\<br /> \,\,\,\,\,\,\,\,\,\,\,\,2x \leqslant 6 \hfill \\<br /> \,\,\,\,\,\,\,\,\,\,\,\,\,\boxed{\,x \leqslant 3} \hfill \\<br /> \hfill \\<br /> i)\,\,\,1 + x \leqslant 2x - 3 \hfill \\<br /> \,\,\,\,\,\,\,\,\,\,\,\,\,\boxed{4 \leqslant x} \hfill \\ <br />\end{gathered} <br />\]<br /><br />](./tex/a3128746e37175076449662f23a9d14b.png)
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May 18 2008, 12:13 PM
Publicado:
#5
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Dios Matemático Supremo Grupo: Baneado Mensajes: 1.737 Registrado: 6-September 07 Miembro Nº: 9.900 |
![TEX: % MathType!MTEF!2!1!+-<br />% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn<br />% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr<br />% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9<br />% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x<br />% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaaI1a<br />% GaaiykaaqaaaqaamaalaaabaGaaGymaaqaaiaaiodaaaGaamiEaiab<br />% gUcaRiaaiwdacqGH+aGpdaWcaaqaaiaaigdaaeaacaaIYaaaaiaadI<br />% hacqGHsislcaaIXaaabaGaaGPaVlaaykW7caaMc8UaaGPaVlaaiwda<br />% cqGHRaWkcaaIXaGaeyOpa4ZaaSaaaeaacaaIXaaabaGaaGOmaaaacq<br />% GHsisldaWcaaqaaiaaigdaaeaacaaIZaaaaaqaaiaaykW7caaMc8Ua<br />% aGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7ca<br />% aI2aGaeyOpa4ZaaSaaaeaacaWG4baabaGaaGOnaaaaaeaacaaMc8Ua<br />% aGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaG4maiaaiAdacq<br />% GH+aGpcaWG4baaaaa!6F9C!<br />\[<br />\begin{gathered}<br /> 5) \hfill \\<br /> \hfill \\<br /> \frac{1}<br />{3}x + 5 > \frac{1}<br />{2}x - 1 \hfill \\<br /> \,\,\,\,5 + 1 > \frac{1}<br />{2} - \frac{1}<br />{3} \hfill \\<br /> \,\,\,\,\,\,\,\,\,\,6 > \frac{x}<br />{6} \hfill \\<br /> \,\,\,\,\,\,\,36 > x \hfill \\ <br />\end{gathered} <br />\]<br />](./tex/c4ccc928f83d4b94cd63c5d078533a89.png)
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May 18 2008, 12:17 PM
Publicado:
#6
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Dios Matemático Supremo Grupo: Baneado Mensajes: 1.737 Registrado: 6-September 07 Miembro Nº: 9.900 |
![TEX: % MathType!MTEF!2!1!+-<br />% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn<br />% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr<br />% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9<br />% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x<br />% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaaI2a<br />% GaaiykaaqaaaqaaiaadIhadaahaaWcbeqaaiaaikdaaaGccqGHsisl<br />% caaI3aGaamiEaiabgUcaRiaaigdacaaIYaGaeyipaWJaaGimaaqaai<br />% aacIcacaWG4bGaeyOeI0IaaGinaiaacMcacaGGOaGaamiEaiabgkHi<br />% TiaaiodacaGGPaGaeyipaWJaaGimaaqaaaqaaiaadMgacaGGPaGaaG<br />% PaVlaaykW7caWG4bGaeyOeI0IaaGinaiabgYda8iaaicdaaeaacaaM<br />% c8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaayk<br />% W7caaMc8UaaGPaVlaaykW7caaMc8+aauIhaeaacaWG4bGaeyipaWJa<br />% aGinaaaaaeaaaeaacaWGPbGaamyAaiaacMcacaaMc8UaaGPaVlaadI<br />% hacqGHsislcaaIZaGaeyipaWJaaGimaaqaaiaaykW7caaMc8UaaGPa<br />% VlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8<br />% UaaGPaVlaaykW7caaMc8+aauIhaeaacaWG4bGaeyipaWJaaG4maaaa<br />% aaaa!8CA9!<br />\[<br />\begin{gathered}<br /> 6) \hfill \\<br /> \hfill \\<br /> x^2 - 7x + 12 < 0 \hfill \\<br /> (x - 4)(x - 3) < 0 \hfill \\<br /> \hfill \\<br /> i)\,\,x - 4 < 0 \hfill \\<br /> \,\,\,\,\,\,\,\,\,\,\,\,\,\boxed{x < 4} \hfill \\<br /> \hfill \\<br /> ii)\,\,x - 3 < 0 \hfill \\<br /> \,\,\,\,\,\,\,\,\,\,\,\,\,\,\boxed{x < 3} \hfill \\ <br />\end{gathered} <br />\]<br />](./tex/9bc93ddac549c131b64c8965b6cdc2c5.png)
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May 18 2008, 12:23 PM
Publicado:
#7
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Dios Matemático Supremo Grupo: Baneado Mensajes: 1.737 Registrado: 6-September 07 Miembro Nº: 9.900 |
7)
![TEX: % MathType!MTEF!2!1!+-<br />% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn<br />% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr<br />% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9<br />% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x<br />% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaaI5a<br />% GaamiEaiabg6da+iaadIhadaahaaWcbeqaaiaaikdaaaGccqGHRaWk<br />% caaIXaGaaGinaaqaaiaaykW7caaMc8UaaGPaVlaaicdacqGH+aGpca<br />% WG4bWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0IaaGyoaiaadIhacqGH<br />% RaWkcaaIXaGaaGinaaqaaiaaykW7caaMc8UaaGPaVlaaicdacqGH+a<br />% GpcaGGOaGaamiEaiabgkHiTiaaiEdacaGGPaGaaiikaiaadIhacqGH<br />% sislcaaIYaGaaiykaaqaaaqaaaqaaiaaykW7caWGPbGaaiykaiaayg<br />% W7caaMc8UaaGPaVlaaykW7caaIWaGaeyOpa4JaamiEaiabgkHiTiaa<br />% iEdaaeaacaaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8<br />% +aauIhaeaacaaI3aGaeyOpa4JaamiEaaaaaeaacaWGPbGaamyAaiaa<br />% cMcacaaMc8UaaGPaVlaaicdacqGH+aGpcaWG4bGaeyOeI0IaaGOmaa<br />% qaaiaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7daqj<br />% EaqaaiaaikdacqGH+aGpcaWG4baaaaaaaa!8C43!<br />\[<br />\begin{gathered}<br /> 9x > x^2 + 14 \hfill \\<br /> \,\,\,0 > x^2 - 9x + 14 \hfill \\<br /> \,\,\,0 > (x - 7)(x - 2) \hfill \\<br /> \hfill \\<br /> \hfill \\<br /> \,i)\,\,\,0 > x - 7 \hfill \\<br /> \,\,\,\,\,\,\,\boxed{7 > x} \hfill \\<br /> ii)\,\,0 > x - 2 \hfill \\<br /> \,\,\,\,\,\,\,\boxed{2 > x} \hfill \\ <br />\end{gathered} <br />\]<br />](./tex/54b8c62e8aa1c81892272dc9daeb8e95.png)
Mensaje modificado por deixo el May 18 2008, 12:39 PM |
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May 18 2008, 12:38 PM
Publicado:
#8
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Dios Matemático Supremo Grupo: Baneado Mensajes: 1.737 Registrado: 6-September 07 Miembro Nº: 9.900 |
![TEX: % MathType!MTEF!2!1!+-<br />% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn<br />% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr<br />% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9<br />% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x<br />% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaaI4a<br />% GaaiykaaqaaaqaaiaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPa<br />% VlaadMhacaGGOaGaamyEaiabgUcaRiaaiAdacaGGPaGaeyOpa4JaaG<br />% OnaaqaaiaadMhadaahaaWcbeqaaiaaikdaaaGccqGHRaWkcaaI2aGa<br />% amyEaiabgkHiTiaaiAdacqGH+aGpcaaIWaaabaaabaGaam4uaiaadg<br />% gacaWGJbGaamyyaiaad6gacaWGKbGaam4BaiaaygW7caaMc8UaamOC<br />% aiaadggacaWGPbGaam4yaiaadwgacaWGZbGaaiOoaaqaaaqaamaala<br />% aabaGaeyOeI0IaaGOnaiabgglaXoaakaaabaGaaG4maiaaiAdacqGH<br />% sislcaaI0aGaaiikaiabgkHiTiaaiAdacqGHflY1caaIXaaaleqaaO<br />% GaaiykaaqaaiaaikdaaaGaeyypa0ZaaSaaaeaacqGHsislcaaI2aGa<br />% eyySae7aaOaaaeaacaaI2aGaaGimaaWcbeaaaOqaaiaaikdaaaGaey<br />% ypa0ZaaSaaaeaaceaIYaGbaybacaGGOaGaeyOeI0IaaG4maiabggla<br />% XoaakaaabaGaaGymaiaaiwdaaSqabaGccaGGPaaabaGabGOmayaawa<br />% aaaiabg2da9iabgkHiTiaaiodacqGHXcqSdaGcaaqaaiaaigdacaaI<br />% 1aaaleqaaaGcbaaabaGaamyAaiaacMcacaaMc8UaaGPaVpaaL4baba<br />% GaamiEaiabg6da+iabgkHiTiaaiodacqGHRaWkdaGcaaqaaiaaigda<br />% caaI1aaaleqaaaaaaOqaaiaadMgacaWGPbGaaiykaiaaykW7caaMc8<br />% +aauIhaeaacaWG4bGaeyOpa4JaeyOeI0IaaG4maiabgkHiTmaakaaa<br />% baGaaGymaiaaiwdaaSqabaaaaaGcbaaaaaa!9ADB!<br />\[<br />\begin{gathered}<br /> 8) \hfill \\<br /> \hfill \\<br /> \,\,\,\,\,\,y(y + 6) > 6 \hfill \\<br /> y^2 + 6y - 6 > 0 \hfill \\<br /> \hfill \\<br /> Sacando\,raices: \hfill \\<br /> \hfill \\<br /> \frac{{ - 6 \pm \sqrt {36 - 4( - 6 \cdot 1} )}}<br />{2} = \frac{{ - 6 \pm \sqrt {60} }}<br />{2} = \frac{{( - 3 \pm \sqrt {15} )}}<br />{{}} = - 3 \pm \sqrt {15} \hfill \\<br /> \hfill \\<br /> i)\,\,\boxed{x > - 3 + \sqrt {15} } \hfill \\<br /> ii)\,\,\boxed{x > - 3 - \sqrt {15} } \hfill \\<br /> \hfill \\ <br />\end{gathered} <br />\]<br />](./tex/a0b71915e4ba632987b91c0e51d0c51e.png)
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May 18 2008, 12:47 PM
Publicado:
#9
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Dios Matemático Supremo Grupo: Baneado Mensajes: 1.737 Registrado: 6-September 07 Miembro Nº: 9.900 |
9)
![TEX: <br /><br />% MathType!MTEF!2!1!+-<br />% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn<br />% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr<br />% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9<br />% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x<br />% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWG4b<br />% WaaWbaaSqabeaacaaIYaaaaOGaeyOeI0IaaGOmaiaadIhacqGHRaWk<br />% caaIXaGaeyipaWJaaGimaaqaaiaaykW7caaMc8UaaGPaVlaaykW7ca<br />% aMc8UaaGPaVlaacIcacaWG4bGaeyOeI0IaaGymaiaacMcadaahaaWc<br />% beqaaiaaikdaaaGccqGH8aapcaaIWaaabaGaae4uaiaabMgacaqGUb<br />% GaaeiiaiaabofacaqGVbGaaeiBaiaabwhacaqGJbGaaeyAaiaabopa<br />% caqGUbGaaeiiaiaabchacaqGVbGaaeOCaiaabghacaqG1bGaaeyzai<br />% aabccacaqG0bGaae4BaiaabsgacaqGVbGaaeiiaiaab6gacaqG1bGa<br />% aeyBaiaabwgacaqGYbGaae4BaiaabccacaqGHbGaaeiBaiaabccaca<br />% qGJbGaaeyDaiaabggacaqGKbGaaeOCaiaabggacaqGKbGaae4Baiaa<br />% bccacaqGKbGaaeyzaiaabkgacaqGLbGaaeiiaiaabohacaqGLbGaae<br />% OCaiaabccacaqGTbGaaeyyaiaabMhacaqGVbGaaeOCaiaabccacaqG<br />% VbGaaeiiaiaabMgacaqGNbGaaeyDaiaabggacaqGSbGaaeiiaiaabg<br />% gacaqGGaGaae4yaiaabwgacaqGYbGaae4Baaaaaa!8E51!<br />\[<br />\begin{gathered}<br /> x^2 - 2x + 1 < 0 \hfill \\<br /> \,\,\,\,\,\,(x - 1)^2 < 0 \hfill \\<br /> {\text{Sin Soluci\'o n porque todo numero al cuadrado debe ser mayor o igual a cero}} \hfill \\ <br />\end{gathered} <br />\]<br /><br />](./tex/3cd9e61b548d118c35d3cae05e910ab3.png)
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May 18 2008, 06:28 PM
Publicado:
#10
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 Dios Matemático  Grupo: Usuario FMAT Mensajes: 213 Registrado: 17-July 07 Desde: El Barrio de Arellano Miembro Nº: 7.631 Nacionalidad:  Colegio/Liceo:  Universidad:  Sexo:  |
![TEX: \[<br />\begin{gathered}<br /> 10.\quad 4x^2 + 12x + 9 \hfill \\<br /> \left( {x + \frac{3}<br />{2}} \right)^2 > 0 \hfill \\<br /> \hfill \\<br /> \therefore se.cumple\forall x \in \mathbb{R} - \left\{ {\frac{3}<br />{2}} \right\} \hfill \\ <br />\end{gathered} <br />\]<br />](./tex/8cd2379b1f4f78b0e01f70d4211447eb.png) ![TEX: <br />\[<br />\begin{gathered}<br /> 11.x^2 - 10x + 25 \geqslant 0 \hfill \\<br /> (x - 5)^2 \geqslant 0 \hfill \\<br /> se.cumple\forall x \in \mathbb{R} \hfill \\ <br />\end{gathered} <br />\]<br />](./tex/6dfca0c0a71c5853a404329839f4a43a.png) Edit : como el 11 era corto lo deje junto con el 10 xD Mensaje modificado por P e L a O el May 18 2008, 06:31 PM |
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