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3u inequality questions, please help!!! (1 Viewer)

abdullion

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Show full working out, please. It would be very helpful.

1. 1/5x^2-2x-7 < 5/13
2. 1 < 4x-4/2x+3 < 3
 
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FrankXie

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when you have a fraction and don't use latex, you'd better add brackets to avoid confusing
 

Feynman

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For 1, just factor the denominator and multiply both sides by the whole thing squared. Then just deal with the algebra and you'll get (5x-7)(x+1)(5x-8)(5x+6) > 0. Find the roots and plot them on a graph, then sketch the polynomial. Reading the solutions you should get x < -6/5, -1 < x < 7/5 and x > 8/5.

For 2, break it down to two inequalities:

1 < 4x-4/2x+3 and 4x-4/2x+3 < 3

Do these normally and graph them on number planes reading the solutions. Then apply the solutions that satisfy BOTH inequalities. It should be x < -13/2 and x > 7/2.
 

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