What is 4<((74x))/((8x+3))<8 ?

The solution to 4<((74x))/((8x+3))<8 is 2/7 <x< 12/5

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4<((74x))/((8x+3))<8

4 < \frac{( 74 x )}{( 8 x + 3 )} < 8

\frac{2}{7} < x < \frac{12}{5}

Interval Notation

(\frac{2}{7}, \frac{12}{5})

Decimal Notation

0.28571 \dots < x < 2.4

Solution steps

4 < \frac{( 74 x )}{( 8 x + 3 )} < 8

a < u < b

then

a < u and u < b

4 < \frac{( 74 x )}{( 8 x + 3 )} and \frac{( 74 x )}{( 8 x + 3 )} < 8

4 < \frac{74 x}{8 x + 3} : x < - \frac{3}{8} or x > \frac{2}{7}

\frac{74 x}{8 x + 3} < 8 : - \frac{3}{8} < x < \frac{12}{5}

Combine the intervals

(x < - \frac{3}{8} or x > \frac{2}{7}) and - \frac{3}{8} < x < \frac{12}{5}

Merge Overlapping Intervals

\frac{2}{7} < x < \frac{12}{5}

3 x + 2 > 2 x - 4 > x - 11

3 < ∣ 5 - a ∣ < 8

2 (1 - 5 x) - 5 (5 - x) < 10 (5 - x) \leq 4 (5 - 3 x) - (2 - 5 x)

- 3 < 6 x - 11 < 7

\frac{- 25}{6} < \frac{1}{2} - 2 \frac{x}{3} \leq 5

What is 4<((74x))/((8x+3))<8 ?
The solution to 4<((74x))/((8x+3))<8 is 2/7 <x< 12/5