Question

What is the solution of x+4/2x-1<0

Answer 1

`\large\boxed{ -4<x<(1)/(2)\to x\in\left(-4,\ (1)/(2)\right)}`

Explanation:

`Domain:\ 2x-1\\eq0\to x\\eq(1)/(2)`

`(x+4)/(2x-1)<0\iff(x+4)(2x-1)<0\\\\x+4=0\qquad\text{subtract 4 from both sides}\\\\\boxed{x=-4}\\\\2x-1=0\qquad\text{add 1 to both sides}\\\\2x=1\qquad\text{divide both side by 2}\\\\\boxed{x=(1)/(2)}`

`(x+4)(2x-1)=(x)(2x)+....=2x^2+...\to 2>0\\\\\text{therefore the parabola is op}\text{en up}`

`\text{Look at the picture.}`

`(x+4)/(2x-1)<0\iff -4<x<(1)/(2)\to x\in\left(-4,\ (1)/(2)\right)`