## Task B-3.1.

Solve the inequality $1-27^{x} \leqslant 6 \cdot 9^{3 x}$.
## Solution.

Let's write the powers from the inequality with base 3

$$
1-3^{3 x} \leqslant 6 \cdot 3^{6 x}
$$

If we introduce the substitution $t=3^{3 x}$, we get the quadratic inequality $6 t^{2}+t-1 \geqslant 0 . \quad 1$ point

Solving this, we get $t \leqslant-\frac{1}{2}$ or $t \geqslant \frac{1}{3}$.

However, since $t>0$, it must be $t \geqslant \frac{1}{3}$, so we have $3^{3 x} \geqslant 3^{-1}$

and finally $x \geqslant-\frac{1}{3}$.