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How many integer values satisfy (x-1)/3<5/7<(x+4)/5

 Oct 14, 2018
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So we take this first (x-1)/3<5/7 and after this 5/7<(x+4)/5

(x-1)/3 < 5/7                                                5/7<(x+4)/5

7(x-1) < 3(5)                                                5(5) < 7(x+4)

7x - 7 < 15                                                  25 < 7x + 28

7x < 22                                                       -3 < 7x

x<22/7                                                        -3/7 < x 

or x< 3.1...                                                 or x > -0.4...

We find  -0.4 < χ < 3.1 

so the answer : integer values ​​satisfy is 0,1,2,3

Hope this helps!

 Oct 14, 2018
edited by Dimitristhym  Oct 14, 2018

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