Question

solve x for the above​

Answer 1

Step-by-step explanation:

$\frac{2x - 1}{2 {x}^{3} + 3 {x}^{2} + x} > 0 = > \frac{2x - 1}{x(2 {x}^{2} + 3x + 1) } > 0 = >$

$\frac{(2x - 1)}{x(2 {x}^{2} + 2x + x + 1)} = \frac{(2x - 1)}{x(2x(x + 1) + 1(x + 1)} > 0$

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

For the denominator all values of x >0 it has a positive value since x,(x+1) and (2x+1) needs to be greater than 0 implying x>0, x>-1 and x> -1/2. For the numerator to be positive x>1/2. Hence the range for which the given expression is greater than 0 is x€(1/2,infinity) or x>0. Hope it helps you.