1/(3(9x+27))>x+33

Solución

\frac{1}{3 ( 9 x + 27 )} > x + 33

x < - \frac{2 ( 81 + 7 93 )}{9} or - 3 < x < \frac{2 ( 7 93 - 81 )}{9}

Notación de intervalos

(- \infty, - \frac{2 ( 81 + 7 93 )}{9}) \cup (- 3, \frac{2 ( 7 93 - 81 )}{9})

Decimal

x < - 33.00123 \dots or - 3 < x < - 2.99876 \dots

Pasos de solución

\frac{1}{3 ( 9 x + 27 )} > x + 33

Reescribir en la forma estándar

\frac{- 27 x ^{2} - 972 x - 2672}{9 x + 27} > 0

Factorizar

\frac{- 27 x ^{2} - 972 x - 2672}{9 x + 27} : \frac{- ( x - \frac{2 ( 7 93 - 81 )}{9} ) ( x + \frac{2 ( 81 + 7 93 )}{9} )}{9 ( x + 3 )}

\frac{- ( x - \frac{2 ( 7 93 - 81 )}{9} ) ( x + \frac{2 ( 81 + 7 93 )}{9} )}{9 ( x + 3 )} > 0

Simplificar

\frac{- ( x - \frac{2 ( 7 93 - 81 )}{9} ) ( x + \frac{2 ( 81 + 7 93 )}{9} )}{9 ( x + 3 )} > 0

Multiplicar ambos lados por

- 1

(invertir la desigualdad)

\frac{( - ( x - \frac{2 ( 7 93 - 81 )}{9} ) ( x + \frac{2 ( 81 + 7 93 )}{9} ) ) ( - 1 )}{9 ( x + 3 )} < 0 \cdot (- 1)

Simplificar

\frac{( x - \frac{2 ( 7 93 - 81 )}{9} ) ( x + \frac{2 ( 81 + 7 93 )}{9} )}{9 ( x + 3 )} < 0

Multiplicar ambos lados por

9

\frac{9 ( x - \frac{2 ( 7 93 - 81 )}{9} ) ( x + \frac{2 ( 81 + 7 93 )}{9} )}{9 ( x + 3 )} < 0 \cdot 9

Simplificar

\frac{( x - \frac{2 ( 7 93 - 81 )}{9} ) ( x + \frac{2 ( 81 + 7 93 )}{9} )}{x + 3} < 0

Identificar los intervalos

x < - \frac{2 ( 81 + 7 93 )}{9} or - 3 < x < \frac{2 ( 7 93 - 81 )}{9}

\frac{\frac{x}{l o g _{10} ( 1 )}}{2} (2 x + 3) > 0

\frac{( 4 x + 3 )}{( 2 x + 1 )} < 2

(x^{2} + 3 x + 1) (x^{2} + 3 x - 3) \geq 5

(2 x^{2} + 3 x - 5) (3 - 5 x) \geq 0

\frac{( - x ^{2} - 1 )}{( 9 - 2 x )} \leq 0