What is 2/3 < x/5 < 6/7 ?

The solution to 2/3 < x/5 < 6/7 is 10/3 <x< 30/7

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2/3 < x/5 < 6/7

\frac{2}{3} < \frac{x}{5} < \frac{6}{7}

\frac{10}{3} < x < \frac{30}{7}

Interval Notation

(\frac{10}{3}, \frac{30}{7})

Decimal Notation

3.33333 \dots < x < 4.28571 \dots

Solution steps

\frac{2}{3} < \frac{x}{5} < \frac{6}{7}

a < u < b

then

a < u and u < b

\frac{2}{3} < \frac{x}{5} and \frac{x}{5} < \frac{6}{7}

\frac{2}{3} < \frac{x}{5} : x > \frac{10}{3}

\frac{x}{5} < \frac{6}{7} : x < \frac{30}{7}

Combine the intervals

x > \frac{10}{3} and x < \frac{30}{7}

Merge Overlapping Intervals

\frac{10}{3} < x < \frac{30}{7}

h (3) = \frac{3 ^{2} + 9}{10}

2 x^{2} = 24

(2 s^{2} - 5 s t - t^{2}) - (s^{2} + 7 s t - t^{2})

\frac{25 !}{3 ! ( 25 - 3 ) !}

\frac{1}{3} \cdot \frac{1}{5}