What is (-51)/(2-x)< 1/2-3x<= (31)/(2-x) ?

The solution to (-51)/(2-x)< 1/2-3x<= (31)/(2-x) is (13-sqrt(1609))/(12)<= x<2

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(-51)/(2-x)< 1/2-3x<= (31)/(2-x)

\frac{- 51}{2 - x} < \frac{1}{2} - 3 x \leq \frac{31}{2 - x}

\frac{13 - 1609}{12} \leq x < 2

Interval Notation

[\frac{13 - 1609}{12}, 2)

Decimal Notation

- 2.25936 \dots \leq x < 2

Solution steps

\frac{- 51}{2 - x} < \frac{1}{2} - 3 x \leq \frac{31}{2 - x}

a < u \leq b

then

a < u and u \leq b

\frac{- 51}{2 - x} < \frac{1}{2} - 3 x and \frac{1}{2} - 3 x \leq \frac{31}{2 - x}

\frac{- 51}{2 - x} < \frac{1}{2} - 3 x : x < 2

\frac{1}{2} - 3 x \leq \frac{31}{2 - x} : \frac{13 - 1609}{12} \leq x < 2 or x \geq \frac{13 + 1609}{12}

Combine the intervals

x < 2 and (\frac{13 - 1609}{12} \leq x < 2 or x \geq \frac{13 + 1609}{12})

Merge Overlapping Intervals

\frac{13 - 1609}{12} \leq x < 2

- 1 \leq (\frac{1}{3})^{x} < 2

- 1 \leq \frac{x}{( x + 2 )} \leq 3

5 x - 2 < 10 x + 8 < 2 x - 8

x - 1 < x + 3 < 5

0 < ∣ 3 x + 1 ∣ < \frac{1}{3}

What is (-51)/(2-x)< 1/2-3x<= (31)/(2-x) ?
The solution to (-51)/(2-x)< 1/2-3x<= (31)/(2-x) is (13-sqrt(1609))/(12)<= x<2