Actualizar Secuencia Didactica: 12236

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El valor absoluto representa la distancia desde el origen o cero de una recta numérica hasta un número o un punto. Geométricamente los valores absolutos de |x| son números reales de x y es un valor geométrico sin tener en cuenta su signo, sea este positivo (+) o negativo (-). Así, por ejemplo, 5 es el valor absoluto de +5 y de -5. Los valores absolutos están representados por dos líneas verticales, tales como |x| (el cual se lee como módulo de x).Ejemplos:-|5| = 5-|?3| = 3-|4 ? 6| = |?2| = 2 <h2>¿Qué es resolver una ecuación o una inecuación con valor absoluto?</h2> Ejemplo:|????| = 4????1 = 4????2 = ?4 Tenemos dos respuestas para esta ecuación <h2>Ahora, ¿Qué sucede cuando tenemos una inecuación con valor absoluto?</h2> Tenemos dos opciones: <ul><li>1.Menor que o menor o igual que</li></ul> <ul><li>2.Mayor que o mayor o igual que</li></ul> Para poder solucionar inecuaciones con valor absoluto vamos a tener en cuenta las siguientes formulas teniendo en cuenta las dos opciones anteriores de mayor o menor que.<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAoUAAADoCAYAAACZ3J55AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABDRSURBVHhe7d2LkqO4kgDQ8f7/P9eS05W3NQoBEi+DfU6EwgY9DSg7XTXd8/qZ/AMAwFf7v99XAAC+mKQQAABJIQAAkkIAACaSQgAAJIUAAEgKAQCYSAoBAJAUAgAgKQQAYCIpBABAUggAgKQQAICJpBAAAEkhAACSQgAAJpJCAAAkhQAASAoBAJi8fia/7wE+0uv1+n0HcJ2npViSQuDjRVIo1AFXemLcOSwp9E0cuFpv+JIUAlf7+qRQ0AWuMhJzxCfgak+MO/6iCQAAkkIAACSFAABMJIUAAEgKAQCQFAIAMJEUAgAgKQTgvuLfesvSslYP9JMUfrG1YLpWDwB8DkkhAI9Qf0Ht+UJbtqmPw1yb+nxYqkt1m7Ld2nHIc606OJukkH+1AtOcMmC1+i3Vh6X6pbpQ15dt1o5DnmvVAfc1978Lq8/Hvo5zWfJcj2y31resL7X6j+idH84iKWQ2eLXObwmaZf2W/qnVd0Tv3MB95Z6d27tLsaHe92VMACSFFNaCLcATRAzL8kRPXjvPJilkEwEXuFr9E73WT/hyb0fdU38CmGt/8mfgmSSF/KsOPGuBqAxYa23v5slrB/4mflvkni+TxzvzBZYrSQr5jy0B6MlBS8CFz1ImfaP7u9V3JGlcm3u0PsrI/LDXa3rgDnniPLzPk0GpDESpPlfe27JdaNUd1b9W9w1LY4feuXmWuJe992+kLd8hY8GZz8UVc3BfT4w7kkIeS8D9biMxR3yidFXsEKO+2xPjjl8fAwAgKQTgu8RPb674Cc5V88BRJIU8loALAMeRFAIAICkEAEBSCADARFIIAICkEAAASSEAABNJIQAAkkIAACSFAABMJIUAAEgKAQCQFAIAMJEUAgAgKQQAQFIIwId4vV6/78Zs7QefRlJINwEXAD6XpBAAZvhSyzeRFHJrAjLwTj8/P//GIbGIbyAp5JYyCEdABtgqY0kmdeX7XhGHyuRwtH/Zb0t/uIqkkF3qILcn4JVjZRDuUfbLAhCx4MgvlhmXovTGmmyT/eDOJIVsdlTAzeCaQXNkTAEXmFPHhDLO7JXjZAxqKeMTPIGkkM3qQLcl4O4J0gIu0CNjxJGxIuJPxi/4FJJCdtsTcKNPBleAM2R82RtnMlZFidg1GvNy/i2xEq4gKWS3DHT5OiqDawbbreNkPwEXKONJHRNGY0w5TpZR9Zyja4ArSArZJINkBsrS1mBXBtwcu1fddusagM/Sik/1uSXZfqRPrR5jdA1wFUkhu9SB7ahglwE0xlsj4AK1MiaEPB6NDaPtS60562O4E0khm8wFuqOD3dJ4rTnrYwCgj6QQgI+w9QuhL5Lwh6SQbgIuAHwuSSEAAJJCAAAkhQAATCSFAABICgEAkBQCADCRFAIAICkEAEBSCADARFIIAICkEAAASSEAABNJIQAAkkIAACSFAHyI1+v1+27M1n7waSSFdBNwAeBzSQoBYEZ8qc0Cn05SyK0JxMA7/fz8/K9IDvl0kkJuJwNvlAjEAFuV8aQ83qJODnvHKduP9IOrSQrZpQ5yWwNeOU4G3t6EsOybBSBiQW8cGVHGqLV4k/XZHu5MUshmRwTcGCPH2RI0BVxgTh0TylizR8atHG9OGZ/gCSSFbHZEwM32GWBHCLhAj4wRe2NFxqmMW2IPn0ZSyG5HBNwMsBl0swDslbFkS0wp41HGqa1y/j1jwJkkheyWgS5f98igm2VkTAEXSBEPstQxYSSulPFoj3rOkTXAVSSFbJLBNsqegLumNxDXcx65BuC5WvFpb4I3KufMed+xBujxmh7MQ55MD/nnK+9xvA/1caifg6Vno+w3p6fv3Lr4XEvPVW2kLc+19T4v9cuYssSzRcsT446kkG5nBFzYauS58gx+BzGKO3nic+XXxwB8hK1/AEsI4Q9JId0EXAD4XJJCAAAkhQAASAoBAJhICgEAkBQCACApBABgIikEAEBSCACApBAAgImkEAAASSEAAJJCAAAmkkIAACSFAABICgEAmEgKAXi01+v1+445cY3udp3ct/uRFLLKxl0n4H6WvJ9lubO7r+9pjrqeR96XPWNF35+fn38LLJEUdhBwjyXg8gR5T7OIA9/jqL181DhwFUkhlxNw+QSRJGYp5XFdl8fluZayXattXVe+5vuU51p1qXW+Pjc3xtL5fC3rWm1T1s21Waqr7W1b9yvbZMnztfJcXZ99s5TyuFVf15XyXKsu5LlWfZ6bq8vX8n2+5vtQH6fecynHWWrDuV7TH6yH/MkaN7F3qGxb3vi671xd3TfrlsYqle3C2rxL7dfGCtGmNcfcOL3n4zjrs64+LpVjhbrN3Fwh50tLbWuttkvjpaiv24Xy3No4dV2OmcpxSr1jhq19oy6Os02+r8+F+jhl+1J5rq7PcULd74lan3/OSNvQal+eq+vrujBXH+rj1Dpfj72lX9pyrlUf6vN1n7B0PNc31ePV9aWltkt95+p6x2v1n6vvaRvKNiP901Hn4n0o29TnWsd1+/I4lOfm3odW36d54md4208K82JlieO0VBfK+vq41T7V7eq2dX0oX/N9WBurV2vOUJ+vxy7r4319XCrrWm3q+iV123quUs+4rTZzbZfU40Sp11a3yfp4n6/5PvSMme2zPvX0Lduk8ly8r4+3KsfZO9a3yOufJa5bKt+31PVr7Z/ortfgydf6bmtvrees+/rk+/ZJ3pYULj0Aaw/HWQ/lndz1Gjz5Wt9t7a31nHVfn3zf3iWuWVlqZcLYo7d92a5uG+tonT/T0px5/uz1jH7u3nVdfT3LdR015xljvsunfI4nu+1/Uzj6cPS2L9vVbQXcvnl61yXg3sunfI47iGsYz3eWNSPty3at9nnuyvvYmnP0GuzVWkPL6LrWxs26LD1jzsm5yrLXGWO+w+h94xy3TApHH46R9mW7Vvs8F2NepTXn1RuktYaW0XWtjZt1WXrGnJNzlWWvM8Z8h9H7Rr+5Z3vOaPurbVnfXT/TEeuKMXr3zt3v7bv1Xh/X8X3e+t8U9hh9OO7+MG1Z310/0xHrijEE3GP0Xh/Xcb94VuM65vO7prd92a4sqTxXjlP2S62xWnPX7eo2c3Vlv9a4I+o11GPOnW8ZWVfPuOV4WVJdtzRfa5wovcr+ac+Yrb5L69+inmNp/LLt0eug3+3/9nG2y/q5eeba17JdqRw71f3L8VM9Vs+c0SaOR+es+5Rt145DjpXq9qnuF1rjhzjXmivNjTs3Xpqrq+dbGyfMtQ1z/XvHTK2xQ923HndtnLXjUM4RdWWbVv9Qt3uqkc/wCZ+X92g9O54nejzxOXlrUggCLluJOVxBjGKrJz4nt/2LJgDwbvGHevzhXhYJIZ9KUshbCbjA3UVMKgt8qrckhTYVJQEXAN7PTwoBAJAUAgAgKQQAYCIpBABAUggwJ/42/JPtWX/Z9+nXAejz1qRQwP1DwIX7iX357r8Nf5fYENdBnILP97akUMD9S8AFWvwTTcCVvvrXxwIu0NL60ppf3OI1S6muT3lcnw95vFafynZ1XViqC0v1S3Wh/vI61w54rrckhRFMBNz/EnDh/mJfxl7NUu/Tsr4+zrLUp1Wf1sZaG2epfq0v8B1u9ZPCtcBU1tfHWZb6tOrT2lhr4yzVr/UFniH275K1+pYtfXrU447M09P2rHUD73OrpHAtyGwJQmcFrnrckXl62p61buC54gtlWUbt6Qt8vq/+bwprZcDcEjT39AVYE18W69Ir4tKWfsD3kBQWyoA5GjgFXPh8Z3zhO+tL5NK4a3P2rOmsdQPvc7v/pvBoZwWupXHX5uxZ01nrBraLL3yxN7OsfQGs27f69I7ZGitKWhunrF+qa9UD3+E1bf5Ddv9IIGm1zXPxmso2c+OX7UOrT++Y9Vhhrj7HbdUv1YVWfSjPteqBv0b2yJb9VPc5Y08+aZ8/aa1wB0/cM29JCkPd/oyL96Qb8sSHB95pZM9s2V91nzP26JP2/ZPWCnfwxD3jvykEaIhgHkEdCSF8i7clhQLuXwIu3FO5L8/Yo0/Z9+ITfIe3/qRQwP1DwAUA3s2vjwEAkBQCACApBABgIikEAEBSCACApBAAgImkEAAASSEAAJJCAAAmkkIAACSFAABICgEAmEgKAQCQFAIAICkEgC6v1+t/JbXOwVNJCrnM1UFTkIbPcLe9/PPz8/vu7/vy3FHEMK4mKeR0EdiinBE0W66eDzjHt+/l+Nx5DeAKr+mhO2S3+UP4c5UBqfceb+kTsl/2qY/n7J0vjPTj/eLe9d6zkbYco9679fGcK/bk1jlaz1Hv50p1+97+e9acRvqxX1z7p11zSSGL6vu6dp8zAG15FnLs+nXJEfOlnvm4j5H75d5eK693/bok2oSz71O9lp61pVbbLf3r11HRL6z1rcffOh/bPPF6+/Xxl4mHdK2k8n2PaB8bYOsmGA1ee+Yb/WxAv6v38lpJ5ft3GL0uc/JaLX2ed39WnklS+GUymCyVUnm8FmSibbS5KhjtnW/kswHn2bOXo+9aKZXHI/PdKUbktao/W23rZ+V7SQoZ0hOEomTQOjsQHTnf2mcDznN17Eh79v1VawzldclrNWrPZ+U7SArpUga/nkCYQStKBrIeGfBSb7+t84Wy7Ug/YF7spav38ohy3D1zlJ+xR8w1cl2iPvtkGVXOsTYf381fNGFWGTzi3ubx1vu89IzUY++dK/TMF6LNEfNxraX7Wxtpyz71Xjpibx11/3ItIcYbXVvZP4ysqZ6rZ+5oMzJHqVxrjNEzH8fac//eRVIIPNJIzBGfgKs9Me749TEAAJJCAAAkhQAATCSFAABICgEAkBQCADCRFAJAh/gnRrKk1jl4Kkkhl7k6aArS8BnutpfLf3su35/x79FlsimWcRVJIacqg9oV/4jn1fMB57CX/ySaWfJawJn8H01YVQainns82r6UfbNffdxyxHxhtC/vFfeu956NtOUY9d6tj1uu2o9b52k9Rz2fq1S339o/9PQZbc9x4to/7Zr7SSGL8qHOUgaYWtTV7UfUG6gcq+Wo+bLEMbBf7q1U7rWWqK/341nqeeJ4r9715typXEuvbB9lbe1nfFY+m6Twy0RQWCupfN+jDDyjfUP0TdG/PG7ZM9+W9QF9rt7LayWV799h9Lq0lJ9rqf+7PyvP5NfHzKrvaQaZ3vtcB6XRfqPP08h8ez8b71ffwyUjbTnO1n2V/dJR965+DkbWN9e2HrPHyLxptE+9ri1zss+WZ+Pd/KSQISMPeLQtSwals+ydL/oA77d3L4/Ys+/Pjmkxfpa8Fnvs7c/nkxTSpQx+WwNhT0DK4Je2zhV6A+ARnw34r3fs5RFH7fvRtY1cl2iXZY+jPiufz6+PmVUGj7i3eTx3n3uCzVrfrF+bKxwxX4g2PfNxL3HPeu/XSFv2qfdSz97KNkuOuH/lPDFez9pK9TpH1lTPNTr3qL2flf3imj/teksKgUcaiTniE0+UidwSz/V9PTHu+PUxANxQJBRrBY4kKQQAQFIIAICkEACAiaQQAABJIQAAkkIAACaSQgAAJIUAAEgKAQCYSAoBAJAUAgAgKQQAYCIpBABAUggAgKQQAICJpBAAgH9eP5Pf97u8Xq/fdwDX6A1f4hPwDgelWJc5LCkEAOC5/PoYAABJIQAAkkIAACaSQgAAJIUAAEgKAQCYSAoBAJAUAgAgKQQAYCIpBABAUggAgKQQAICJpBAAAEkhAACSQgAAJpJCAAAkhQAASAoBAJhICgEAvt4///w/JrUAAUblzioAAAAASUVORK5CYII=" alt="">Ejemplo 1: - |x| &lt; 5Graficamos, teniendo en cuenta que el valor absoluto me da dos soluciones <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACgAAAATCAYAAADiQ08DAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAACkSURBVEhL7ZWNCoAgDISd7//O5aTFOpY/OUHID0Kmm3esRnQkwsLEa12WbXCU2yAR5UfAuAbmlmrxbow12SAf6lmRGPc8aNUSvWzQKtBIcgmukTzrDqFFS+81fYNvYjNArSWHRHfxMSTaPce9cL312pAerciHVkFN5AstWhLzmuMUVJ1IMlNLR8FeUMv1XzxqzmLJIdG4GvTuHvOvDs5gGxwjhBOhKWY59c9WtQAAAABJRU5ErkJggg==" alt=""> por lo tanto <img src="data:image/png;base64,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" alt=""><img src="data:image/png;base64,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" alt="">Ahora bien, ¿cómo sabemos que esa respuesta es la correcta?, si reemplazamos cualquiera de esos valores del intervalo (-5, 5) en la inecuacion dada cumple con la condición. |????| &lt; 5|4| &lt; 54 &lt; 5 Solución: ????? &lt; ???? &lt; ????Ejemplo 2:Recordemos que para resolver una ecuación debemos encontrar el valor de la ???? para que la expresión sea verdadera. Ejemplo:<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARwAAAA0CAYAAABYfIcPAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAANKSURBVHhe7dwNj5swDIDh6/7/f97mUy0hC/JBYoeY95EQR1dIiB0X6N0+f//7AYAAf75rAHBHwQEQhoIDIAwFBwj0+Xy+P7W7s88Iz/YoOMCLSXGxiycKzk3egQGiyBfVdvGSouB4T/5j9dcFQL9HFZw7Ezlq8kd+CuBd7IeY3c5k6yscCQoTHzuzOazbrXmtxam01PS+f4TLbxprp/XQdvuKvO9Od+7u18r7+HiPq1wqzZHo/PNsb/oVju2sbkcO2BnpR20p6XkvgHNuf0ulk7J0+JaJ29I9OU50QVvRJvZ3lTel+VLKNd2vpDdPPXN76TMcOanjcvUakJmd4C1FRNn5craU9LQ1Q4qvxVvIwNYWIJLm3bEo2O0I2o+z/szm9tBYDmvXNXdP1n2QTo7v3SZyupM3mXJt6hWODIwdHM/B0vbszx70+LpQbIB+/AdcAMK85hkOgPUoOADCUHAAhKHgAAhDwQHwy/NbXsW3VAP4ehy7uiou3vlMwWm0IkAUNHhZlVvcUnWQANnFy1WBA3ZGwXkgrmzykxgfP1Tsdlbb31JpkPQ07PYsctzooVrRJvxpXO36qCX28p6aq2Oc7Vtrb4atC44NWC1IuwWodj7Ym+aUjfHV694i8i3FQ+MnBkj7VFLrb0QCYJ1S3q6IfUSbFJwB3gFakXSIU8rbltjr/iU9+RORb68qOLsFKCIBsIbG1q7VitzyblOkeGgsp2DXs60IkPfxEU9iKjSudltF5JYVkWvbFpzWwM0SGaBVyYBnOMY/W9xT3FIB2AO/+AcgDAUHQBgKDoAwFBwAYSg4AMJQcAB0Ofu1jVZ8LT5IBp8hRFZXxeVuzlNwBmgwGEJkNfsDlVuqm7iyAfqlKThSAI6Xf3YbeIo352qKWyoJlpyGXV9pCW5tf/33WlvAkc3Rs/yR10Qpr/Q9JTPy8qydkeOmeobTEqhRNkF0274OlFzlakQ+adslpbZH+kbB6VQKVqKhhLNaro5Mam8UnK/WglMqGqp1WJ6cGHiuUq625NTMHO41kvNpCo4Ogl17i2oHedRy9Uk5ddaXkf5tX3Dk5IWeht32pG2JzYcRAVpyVV6TbV2vdsxxNdKvVLdUwO6OEzzf1Pz5+QfT+aaotdaJiAAAAABJRU5ErkJggg==" alt="">Ahora con inecuaciones|????| &gt; ????Vamos a ver cual seria la solución de |????| &gt; 3 gráficamente y luego teniendo en cuenta la formula (propiedad) enunciada anteriormente para mayor que, de esta manera tenemos: <img src="data:image/png;base64,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" alt="">Esto quiere decir que todos los números que están después de 3 son respuesta o cumplen con la condición de la inecuación, al igual que todos los numeros que son menos que -3.Por lo tanto tenemos que nuestra solución es ???? &lt; ?3 ???? ???? &gt; 3 o los intervalos (??, ?3) ???? (3, ?)Ahora, haciendo uso de la formula (propiedad), tenemos lo siguiente:<img src="data:image/png;base64,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" alt="">En intervalos (??, ?3) ???? (3, ?)Ejemplo 3:Resolver la siguiente inecuación con valor absoluto |???? + 5| ? 3Para aplicar la formula tenemos en cuenta quien es nuestra ???? y quien sería nuestro ????<img src="data:image/png;base64,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" alt="">Reemplazamos en la formula de la siguiente manera<img src="data:image/png;base64,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" alt="">Solución (??, ?8] ???? [?2, ?) Ejemplo 4: Resolver la siguiente inecuación con valor absoluto |???? ? 3| ? 12<img src="data:image/png;base64,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" alt="">Para aplicar la formula tenemos en cuenta quien es nuestra ???? y quine sería nuestro ???? <img src="data:image/png;base64,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" 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