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TNSKermit

Let's solve your inequality step-by-step.

x2+9x−22/x+4  >0

Let's find the critical points of the inequality.

x2+9x−22/x+4  =0

x2+9x−22=0(Multiply both sides by x+4)

(x−2)(x+11)=0(Factor left side of equation)

x−2=0 or x+11=0(Set factors equal to 0)

x=2 or x=−11

Check possible critical points.

x=2(Works in original equation)

x=−11(Works in original equation)

Critical points:

x=2 or x=−11(Makes both sides equal)

x=−4(Makes left denominator equal to 0)

Check intervals in between critical points. (Test values in the intervals to see if they work.)

x<−11(Doesn't work in original inequality)

−11<x<−4(Works in original inequality)

−4<x<2(Doesn't work in original inequality)

x>2(Works in original inequality)

Answer:

−11<x<−4 or x>2~

Following are the calculation to the given equation:

Given:

[tex]\frac{x^2+9x-22}{x+4}\geq 0[/tex]

To find:

graph set=?

Solution:

[tex]\to \frac{x^2+9x-22}{x+4} \geq 0\\\\\to \frac{x^2+(11-2)x-22}{x+4}\geq0\\\\\to \frac{x^2+11x-2x-22}{x+4}\geq0\\\\\to \frac{x(x+11)-2(x+11)}{x+4} \geq0\\\\\to \frac{(x+11)(x-2)}{x+4}\geq 0\\\\[/tex]

The answer is "Option 3".

Learn more:

brainly.com/question/23333288

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