3^-x+3>3 desigualdades

Se da la desigualdad:
$$3 + 3^{- x} > 3$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$3 + 3^{- x} = 3$$
Resolvemos:
$$x_{1} = 91.2951886379681$$
$$x_{2} = 93.2951886379681$$
$$x_{3} = 47.295188637968$$
$$x_{4} = 59.295188637968$$
$$x_{5} = 87.2951886379681$$
$$x_{6} = 45.295188637968$$
$$x_{7} = 71.2951886379681$$
$$x_{8} = 61.295188637968$$
$$x_{9} = 95.2951886379681$$
$$x_{10} = 65.2951886379681$$
$$x_{11} = 117.295188637968$$
$$x_{12} = 69.2951886379681$$
$$x_{13} = 67.2951886379681$$
$$x_{14} = 43.295188637968$$
$$x_{15} = 25.295188637968$$
$$x_{16} = 79.2951886379681$$
$$x_{17} = 51.295188637968$$
$$x_{18} = 99.2951886379681$$
$$x_{19} = 31.295188637968$$
$$x_{20} = 49.295188637968$$
$$x_{21} = 113.295188637968$$
$$x_{22} = 77.2951886379681$$
$$x_{23} = 33.295188637968$$
$$x_{24} = 41.295188637968$$
$$x_{25} = 107.295188637968$$
$$x_{26} = 103.295188637968$$
$$x_{27} = 83.2951886379681$$
$$x_{28} = 35.295188637968$$
$$x_{29} = 27.295188637968$$
$$x_{30} = 97.2951886379681$$
$$x_{31} = 37.295188637968$$
$$x_{32} = 63.295188637968$$
$$x_{33} = 85.2951886379681$$
$$x_{34} = 111.295188637968$$
$$x_{35} = 109.295188637968$$
$$x_{36} = 81.2951886379681$$
$$x_{37} = 29.295188637968$$
$$x_{38} = 75.2951886379681$$
$$x_{39} = 119.295188637968$$
$$x_{40} = 115.295188637968$$
$$x_{41} = 55.295188637968$$
$$x_{42} = 53.295188637968$$
$$x_{43} = 101.295188637968$$
$$x_{44} = 39.295188637968$$
$$x_{45} = 105.295188637968$$
$$x_{46} = 73.2951886379681$$
$$x_{47} = 57.295188637968$$
$$x_{48} = 89.2951886379681$$
$$x_{1} = 91.2951886379681$$
$$x_{2} = 93.2951886379681$$
$$x_{3} = 47.295188637968$$
$$x_{4} = 59.295188637968$$
$$x_{5} = 87.2951886379681$$
$$x_{6} = 45.295188637968$$
$$x_{7} = 71.2951886379681$$
$$x_{8} = 61.295188637968$$
$$x_{9} = 95.2951886379681$$
$$x_{10} = 65.2951886379681$$
$$x_{11} = 117.295188637968$$
$$x_{12} = 69.2951886379681$$
$$x_{13} = 67.2951886379681$$
$$x_{14} = 43.295188637968$$
$$x_{15} = 25.295188637968$$
$$x_{16} = 79.2951886379681$$
$$x_{17} = 51.295188637968$$
$$x_{18} = 99.2951886379681$$
$$x_{19} = 31.295188637968$$
$$x_{20} = 49.295188637968$$
$$x_{21} = 113.295188637968$$
$$x_{22} = 77.2951886379681$$
$$x_{23} = 33.295188637968$$
$$x_{24} = 41.295188637968$$
$$x_{25} = 107.295188637968$$
$$x_{26} = 103.295188637968$$
$$x_{27} = 83.2951886379681$$
$$x_{28} = 35.295188637968$$
$$x_{29} = 27.295188637968$$
$$x_{30} = 97.2951886379681$$
$$x_{31} = 37.295188637968$$
$$x_{32} = 63.295188637968$$
$$x_{33} = 85.2951886379681$$
$$x_{34} = 111.295188637968$$
$$x_{35} = 109.295188637968$$
$$x_{36} = 81.2951886379681$$
$$x_{37} = 29.295188637968$$
$$x_{38} = 75.2951886379681$$
$$x_{39} = 119.295188637968$$
$$x_{40} = 115.295188637968$$
$$x_{41} = 55.295188637968$$
$$x_{42} = 53.295188637968$$
$$x_{43} = 101.295188637968$$
$$x_{44} = 39.295188637968$$
$$x_{45} = 105.295188637968$$
$$x_{46} = 73.2951886379681$$
$$x_{47} = 57.295188637968$$
$$x_{48} = 89.2951886379681$$
Las raíces dadas
$$x_{15} = 25.295188637968$$
$$x_{29} = 27.295188637968$$
$$x_{37} = 29.295188637968$$
$$x_{19} = 31.295188637968$$
$$x_{23} = 33.295188637968$$
$$x_{28} = 35.295188637968$$
$$x_{31} = 37.295188637968$$
$$x_{44} = 39.295188637968$$
$$x_{24} = 41.295188637968$$
$$x_{14} = 43.295188637968$$
$$x_{6} = 45.295188637968$$
$$x_{3} = 47.295188637968$$
$$x_{20} = 49.295188637968$$
$$x_{17} = 51.295188637968$$
$$x_{42} = 53.295188637968$$
$$x_{41} = 55.295188637968$$
$$x_{47} = 57.295188637968$$
$$x_{4} = 59.295188637968$$
$$x_{8} = 61.295188637968$$
$$x_{32} = 63.295188637968$$
$$x_{10} = 65.2951886379681$$
$$x_{13} = 67.2951886379681$$
$$x_{12} = 69.2951886379681$$
$$x_{7} = 71.2951886379681$$
$$x_{46} = 73.2951886379681$$
$$x_{38} = 75.2951886379681$$
$$x_{22} = 77.2951886379681$$
$$x_{16} = 79.2951886379681$$
$$x_{36} = 81.2951886379681$$
$$x_{27} = 83.2951886379681$$
$$x_{33} = 85.2951886379681$$
$$x_{5} = 87.2951886379681$$
$$x_{48} = 89.2951886379681$$
$$x_{1} = 91.2951886379681$$
$$x_{2} = 93.2951886379681$$
$$x_{9} = 95.2951886379681$$
$$x_{30} = 97.2951886379681$$
$$x_{18} = 99.2951886379681$$
$$x_{43} = 101.295188637968$$
$$x_{26} = 103.295188637968$$
$$x_{45} = 105.295188637968$$
$$x_{25} = 107.295188637968$$
$$x_{35} = 109.295188637968$$
$$x_{34} = 111.295188637968$$
$$x_{21} = 113.295188637968$$
$$x_{40} = 115.295188637968$$
$$x_{11} = 117.295188637968$$
$$x_{39} = 119.295188637968$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{15}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{15} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 25.295188637968$$
=
$$25.195188637968$$
lo sustituimos en la expresión
$$3 + 3^{- x} > 3$$
$$3^{- 25.195188637968} + 3 > 3$$

3.00000000000095 > 3

significa que una de las soluciones de nuestra ecuación será con:
$$x < 25.295188637968$$

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       x15      x29      x37      x19      x23      x28      x31      x44      x24      x14      x6      x3      x20      x17      x42      x41      x47      x4      x8      x32      x10      x13      x12      x7      x46      x38      x22      x16      x36      x27      x33      x5      x48      x1      x2      x9      x30      x18      x43      x26      x45      x25      x35      x34      x21      x40      x11      x39

Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < 25.295188637968$$
$$x > 27.295188637968 \wedge x < 29.295188637968$$
$$x > 31.295188637968 \wedge x < 33.295188637968$$
$$x > 35.295188637968 \wedge x < 37.295188637968$$
$$x > 39.295188637968 \wedge x < 41.295188637968$$
$$x > 43.295188637968 \wedge x < 45.295188637968$$
$$x > 47.295188637968 \wedge x < 49.295188637968$$
$$x > 51.295188637968 \wedge x < 53.295188637968$$
$$x > 55.295188637968 \wedge x < 57.295188637968$$
$$x > 59.295188637968 \wedge x < 61.295188637968$$
$$x > 63.295188637968 \wedge x < 65.2951886379681$$
$$x > 67.2951886379681 \wedge x < 69.2951886379681$$
$$x > 71.2951886379681 \wedge x < 73.2951886379681$$
$$x > 75.2951886379681 \wedge x < 77.2951886379681$$
$$x > 79.2951886379681 \wedge x < 81.2951886379681$$
$$x > 83.2951886379681 \wedge x < 85.2951886379681$$
$$x > 87.2951886379681 \wedge x < 89.2951886379681$$
$$x > 91.2951886379681 \wedge x < 93.2951886379681$$
$$x > 95.2951886379681 \wedge x < 97.2951886379681$$
$$x > 99.2951886379681 \wedge x < 101.295188637968$$
$$x > 103.295188637968 \wedge x < 105.295188637968$$
$$x > 107.295188637968 \wedge x < 109.295188637968$$
$$x > 111.295188637968 \wedge x < 113.295188637968$$
$$x > 115.295188637968 \wedge x < 117.295188637968$$
$$x > 119.295188637968$$