What is 1/4 < x/5 < 2/3 ?

The solution to 1/4 < x/5 < 2/3 is 5/4 <x< 10/3

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1/4 < x/5 < 2/3

\frac{1}{4} < \frac{x}{5} < \frac{2}{3}

\frac{5}{4} < x < \frac{10}{3}

Interval Notation

(\frac{5}{4}, \frac{10}{3})

Decimal Notation

1.25 < x < 3.33333 \dots

Solution steps

\frac{1}{4} < \frac{x}{5} < \frac{2}{3}

a < u < b

then

a < u and u < b

\frac{1}{4} < \frac{x}{5} and \frac{x}{5} < \frac{2}{3}

\frac{1}{4} < \frac{x}{5} : x > \frac{5}{4}

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

Combine the intervals

x > \frac{5}{4} and x < \frac{10}{3}

Merge Overlapping Intervals

\frac{5}{4} < x < \frac{10}{3}

6 a + 3 = 45

\frac{2 ^{n + 1}}{2 ^{n}}

x + 1 \cdot x - 1

3 w^{2} - 8 w - 3

3 m^{2} - 3 m - 64 = - 4