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mathmath333
 one year ago
Find the range of \(x\)
mathmath333
 one year ago
Find the range of \(x\)

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1\(\large \color{black}{\begin{align} (2x+3)(x5)<0\hspace{.33em}\\~\\ \end{align}}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1the parabola cuts the x axis at points 3/2 and 5 so it looks like this dw:1433764773998:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{3}{2}~\lt~x\lt~5\]

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1But if i evaluate individually \((2x+3)<0\) and \((x5)<0\) then it comes as \(x<\dfrac{3}{2}\) and \(x<5\) so it should be \(x<5\) ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1product of two negatives always gives you > 0

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\[a*b \lt 0 \] implies \[a\lt 0,~\text{and}~ b\gt 0\] or \[a\gt 0,~\text{and}~b\lt 0\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\[(2x+3)*(x5) \lt 0 \] implies \[(2x+3)\lt 0,~\text{and}~ (x5)\gt 0\] or \[(2x+3)\gt 0,~\text{and}~(x5)\lt 0\]

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1so by the above as u stated it can also be \(x<\dfrac{3}{2}\) and \(x>5\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Yes, but are there any numbers in real that are both less than 3/2 and greater than 5 ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1so that case yields an emptyset

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1we work the other case

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1is that the only algebraic method u stated

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1i don't like algebraic method when the product has only 2 factors i prefer visualizing a parabola

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1because the x intercepts are readily avilable when you're given the inequality in product form

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433765981235:dw how did u visualize the shaded region

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\[\large \color{black}{\begin{align} (2x+3)(x5)\color{red}{<}0\hspace{.33em}\\~\\ \end{align}}\] you want the product to be less than 0 so just shade the region below x axis

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@mathmath333 that isnt you in your profile picture :)
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