What is 4<(3x-10)/(x+7)<24 ?

The solution to 4<(3x-10)/(x+7)<24 is -38<x<-178/21

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4<(3x-10)/(x+7)<24

4 < \frac{3 x - 10}{x + 7} < 24

- 38 < x < - \frac{178}{21}

Solution steps

4 < \frac{3 x - 10}{x + 7} < 24

a < u < b

then

a < u and u < b

4 < \frac{3 x - 10}{x + 7} and \frac{3 x - 10}{x + 7} < 24

4 < \frac{3 x - 10}{x + 7} : - 38 < x < - 7

\frac{3 x - 10}{x + 7} < 24 : x < - \frac{178}{21} or x > - 7

Combine the intervals

- 38 < x < - 7 and (x < - \frac{178}{21} or x > - 7)

Merge Overlapping Intervals

- 38 < x < - \frac{178}{21}

8 ln (1)

\frac{x + 1}{x} < 1

7 = - 7 - y

\frac{6 x + 1}{4} \leq x + 1

x^{2} + 14 x + 49

What is 4<(3x-10)/(x+7)<24 ?
The solution to 4<(3x-10)/(x+7)<24 is -38<x<-178/21