Resolver em R a inequação
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Boa noite Gab!
Solução!
![\bigg( \dfrac{2}{7}\bigg)^{1-x} \leq \bigg( \dfrac{7}{2}\bigg)^{2x+3}\\\\\\
Invertendo ~~a~~ base ~~vai ~~ficar~~ com~~ o~expoente~~ negativo\\\\\\\
\bigg( \dfrac{7}{2}^{-1} \bigg) ^{1-x} \leq \bigg( \dfrac{7}{2}\bigg)^{2x+3}\\\\\\\\\
-1(1-x) \leq 2x+3\\\\\\
-1+x \leq 2x+3\\\\\
x-2x \leq 3+1\\\\\\
-x \leq 4\\\\\\
\boxed{x \leq -4}\\\\\\\
S=\{x \in \mathbb{R}| x~~~~x \leq -4\}](https://tex.z-dn.net/?f=%5Cbigg%28+%5Cdfrac%7B2%7D%7B7%7D%5Cbigg%29%5E%7B1-x%7D++%5Cleq+%5Cbigg%28+%5Cdfrac%7B7%7D%7B2%7D%5Cbigg%29%5E%7B2x%2B3%7D%5C%5C%5C%5C%5C%5C%0AInvertendo+%7E%7Ea%7E%7E+base+%7E%7Evai+%7E%7Eficar%7E%7E+com%7E%7E+o%7Eexpoente%7E%7E+negativo%5C%5C%5C%5C%5C%5C%5C%0A%5Cbigg%28+%5Cdfrac%7B7%7D%7B2%7D%5E%7B-1%7D+%5Cbigg%29+%5E%7B1-x%7D++%5Cleq+%5Cbigg%28+%5Cdfrac%7B7%7D%7B2%7D%5Cbigg%29%5E%7B2x%2B3%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C+%0A-1%281-x%29+%5Cleq+2x%2B3%5C%5C%5C%5C%5C%5C%0A-1%2Bx+%5Cleq+2x%2B3%5C%5C%5C%5C%5C%0Ax-2x+%5Cleq+3%2B1%5C%5C%5C%5C%5C%5C%0A-x+%5Cleq+4%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7Bx+%5Cleq+-4%7D%5C%5C%5C%5C%5C%5C%5C%0AS%3D%5C%7Bx+%5Cin+%5Cmathbb%7BR%7D%7C+x%7E%7E%7E%7Ex+%5Cleq+-4%5C%7D%0A+ "\bigg( \dfrac{2}{7}\bigg)^{1-x} \leq \bigg( \dfrac{7}{2}\bigg)^{2x+3}\\\\\\
Invertendo ~~a~~ base ~~vai ~~ficar~~ com~~ o~expoente~~ negativo\\\\\\\
\bigg( \dfrac{7}{2}^{-1} \bigg) ^{1-x} \leq \bigg( \dfrac{7}{2}\bigg)^{2x+3}\\\\\\\\\
-1(1-x) \leq 2x+3\\\\\\
-1+x \leq 2x+3\\\\\
x-2x \leq 3+1\\\\\\
-x \leq 4\\\\\\
\boxed{x \leq -4}\\\\\\\
S=\{x \in \mathbb{R}| x~~~~x \leq -4\}")
Boa noite!
Bons estudos!
Solução!
Boa noite!
Bons estudos!
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