What is 4/11 < x/(20)< 5/11 ?

The solution to 4/11 < x/(20)< 5/11 is 80/11 <x< 100/11

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4/11 < x/(20)< 5/11

\frac{4}{11} < \frac{x}{20} < \frac{5}{11}

\frac{80}{11} < x < \frac{100}{11}

Interval Notation

(\frac{80}{11}, \frac{100}{11})

Decimal Notation

7.27272 \dots < x < 9.09090 \dots

Solution steps

\frac{4}{11} < \frac{x}{20} < \frac{5}{11}

a < u < b

then

a < u and u < b

\frac{4}{11} < \frac{x}{20} and \frac{x}{20} < \frac{5}{11}

\frac{4}{11} < \frac{x}{20} : x > \frac{80}{11}

\frac{x}{20} < \frac{5}{11} : x < \frac{100}{11}

Combine the intervals

x > \frac{80}{11} and x < \frac{100}{11}

Merge Overlapping Intervals

\frac{80}{11} < x < \frac{100}{11}

- 1 < 1 - x < 0

3 < x + 1 < 7

- 2 < x + 3 < 4

- 4 \leq 3 x - 1 < 8

3 x + 2 < ∣ 2 x + 5 ∣ < 8 x + 9

What is 4/11 < x/(20)< 5/11 ?
The solution to 4/11 < x/(20)< 5/11 is 80/11 <x< 100/11