What is 1/3 >(x-1)/5 > 1/9 ?

The solution to 1/3 >(x-1)/5 > 1/9 is 14/9 <x< 8/3

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1/3 >(x-1)/5 > 1/9

\frac{1}{3} > \frac{x - 1}{5} > \frac{1}{9}

\frac{14}{9} < x < \frac{8}{3}

Interval Notation

(\frac{14}{9}, \frac{8}{3})

Decimal Notation

1.55555 \dots < x < 2.66666 \dots

Solution steps

\frac{1}{3} > \frac{x - 1}{5} > \frac{1}{9}

a > u > b

then

a > u and u > b

\frac{1}{3} > \frac{x - 1}{5} and \frac{x - 1}{5} > \frac{1}{9}

\frac{1}{3} > \frac{x - 1}{5} : x < \frac{8}{3}

\frac{x - 1}{5} > \frac{1}{9} : x > \frac{14}{9}

Combine the intervals

x < \frac{8}{3} and x > \frac{14}{9}

Merge Overlapping Intervals

\frac{14}{9} < x < \frac{8}{3}

\frac{x}{4} + \frac{x}{7} = - 3

- 8 x + 1 \leq - 7 x - 9

\frac{v}{8} = 2

4^{x - 2} > 15

\frac{3}{5} + y \geq \frac{11}{15}