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Find all real values of x such that \(\frac{x^2 + x + 3}{2x^2 + x - 6} \ge 0.\)

 May 21, 2022
 #1
avatar+588 
+2

The solution can be written in multiple ways. Find the best way that you need.

 

 \begin{bmatrix}\mathrm{Solution:}\:&\:x<-2\quad \mathrm{or}\quad \:x>\frac{3}{2}\:\\ \:\mathrm{Decimal:}&\:x<-2\quad \mathrm{or}\quad \:x>1.5\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-2\right)\cup \left(\frac{3}{2},\:\infty \:\right)\end{bmatrix}

 May 21, 2022
 #2
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+1

Can you please show how you got that, i'm not quite understanding.

Guest May 21, 2022
 #3
avatar+588 
+2

Ok.

So if u take the equation and then factor the equation u should get

x^2+x+3/(2x-3)(x+2)

 

Once you get that then find the intervals:

Look at the circled numbers and those are the intervals (or you can all them the answers) and then the answer I wrote previously was ways you can write it!!

Hope this helped!!

 May 21, 2022
 #4
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+1

Thank you!

 May 22, 2022

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