Question

Solve the following inequality:
${\log }_{0.5}(1+2x)>-1$

Answer 1

$1+2x>0x>-\frac{1}{2}$

and

$\frac{\log (1+2x)}{\log \left(0.5\right)}>-1\frac{-\log (1+2x)}{\log \left(2\right)}>-1-\log (1+2x)>-\log \left(2\right)1+2x<22x<1x<\frac{1}{2}$

Taking intersection, we get

$x\in (-\frac{1}{2},\frac{1}{2})$