Respuesta :

gmany

Answer:

[tex]\large\boxed{ -4<x<\frac{1}{2}\to x\in\left(-4,\ \dfrac{1}{2}\right)}[/tex]

Step-by-step explanation:

[tex]Domain:\ 2x-1\neq0\to x\neq\dfrac{1}{2}[/tex]

[tex]\dfrac{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=\dfrac{1}{2}}[/tex]

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

[tex]\text{Look at the picture.}[/tex]

[tex]\dfrac{x+4}{2x-1}<0\iff -4<x<\frac{1}{2}\to x\in\left(-4,\ \dfrac{1}{2}\right)[/tex]

Ver imagen gmany

Answer:

[tex]x \in \bigg(-4,\displaystyle\frac{1}{2}\bigg)[/tex]    

Step-by-step explanation:

We are given the following information in the question:

[tex]\displaystyle\frac{x + 4}{2x-1} < 0[/tex]

Domain of given function:

[tex]2x - 1 \neq 0\\x \neq \displaystyle\frac{1}{2}[/tex]

Th function is not defined on [tex]\frac{1}{2}[/tex]

To solve the above inequality, we take the following steps:

[tex]\displaystyle\frac{x + 4}{2x-1} < 0\\\\x + 4 > 0 \text{ and } 2x-1 < 0\\x > -4\\2x - 1 <0\\2x < 1\\x < \frac{1}{2}\\[/tex]

In interval notation it can be written as:

[tex]x \in \bigg(-4,\displaystyle\frac{1}{2}\bigg)[/tex]

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