[tex]\Large\begin{aligned}\\&\!\left(\dfrac{1}{7}\right)^x+\left(\dfrac{1}{7}\right)^{x+1}\geq56\\&\!\left(\dfrac{1}{7}\right)^x\left(1+\dfrac{1}{7}\right)\geq56\\&\!\left(\dfrac{1}{7}\right)^x\cdot\dfrac{8}{7}\geq56\\&\!\left(\dfrac{1}{7}\right)^x\geq7^2\\&\,7^{-x}\geq7^2\\&\,-x\geq2\\&\,\, x\leq-2\end{aligned}[/tex]
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[tex]\Large\begin{aligned}\\&\!\left(\dfrac{1}{7}\right)^x+\left(\dfrac{1}{7}\right)^{x+1}\geq56\\&\!\left(\dfrac{1}{7}\right)^x\left(1+\dfrac{1}{7}\right)\geq56\\&\!\left(\dfrac{1}{7}\right)^x\cdot\dfrac{8}{7}\geq56\\&\!\left(\dfrac{1}{7}\right)^x\geq7^2\\&\,7^{-x}\geq7^2\\&\,-x\geq2\\&\,\, x\leq-2\end{aligned}[/tex]