Question

Решите уравнение (1/2)^x+2 +3*(1/2)^x+1 -(1/2)^x<3

Answer 1

$\left ( \frac{1}{2} \right )^{x+2}+3\left ( \frac{1}{2} \right )^{x+1}-\left ( \frac{1}{2} \right )^x\Leftrightarrow \\\\\Leftrightarrow \left ( \frac{1}{2} \right )^x\left ( \frac{1}{4}+\frac{3}{2}-1 \right )<3\Leftrightarrow \left ( \frac{1}{2} \right )^x<4\Leftrightarrow \\\\\Leftrightarrow 2^{-x}<2^2\Rightarrow x>-2$