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Find the interval of all x such that \frac{-2x+5}{7} is in the interval [0,1).

 Oct 4, 2020
 #1
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The solution is [3/4,11/4).

 Oct 4, 2020
 #2
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Find the interval of all x such that \frac{-2x+5}{7} is in the interval [0,1).

 

\(0\le \frac{-2x+5}{7}<1\\ 0\le -2x+5<7\\ -5\le -2x < 2 \)

 

Now it gets a little trickier because when you divide or multiply by a negative number you have to turn the inequalities around.

So you need to separate the two.

 

\(-5\le-2x \;\;and\;\; -2x<2\\ \frac{5}{2}\ge x \qquad \;\;and\;\;\;\; x>-1\\ x\le \frac{5}{2} \qquad \;\;and\;\;\;\; x>-1\\\)

Now all you have to do is work out where these two intersect.

 Oct 4, 2020

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