Question

Решите неравенство: log0,5(1+2х)≥-2

Answer 1

ОДЗ :

1 + 2x > 0

2x > - 1

x > - 0,5

$log_{0,5}(1+2x)\geq -2\\\\0<0,5<1\Rightarrow 1+2x\leq (0,5)^{-2}\\\\1+2x\leq 4\\\\2x\leq 3\\\\x\leq 1,5\\\\Otvet:\boxed{x\in(-0,5;1,5]}$