What is 0<= (1-x)/(2x-1)<3 ?

The solution to 0<= (1-x)/(2x-1)<3 is 4/7 <x<= 1

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0<= (1-x)/(2x-1)<3

0 \leq \frac{1 - x}{2 x - 1} < 3

\frac{4}{7} < x \leq 1

Interval Notation

(\frac{4}{7}, 1]

Decimal Notation

0.57142 \dots < x \leq 1

Solution steps

0 \leq \frac{1 - x}{2 x - 1} < 3

a \leq u < b

then

a \leq u and u < b

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

0 \leq \frac{1 - x}{2 x - 1} : \frac{1}{2} < x \leq 1

\frac{1 - x}{2 x - 1} < 3 : x < \frac{1}{2} or x > \frac{4}{7}

Combine the intervals

\frac{1}{2} < x \leq 1 and (x < \frac{1}{2} or x > \frac{4}{7})

Merge Overlapping Intervals

\frac{4}{7} < x \leq 1

\frac{9 !}{( 9 - 5 ) ! \cdot 5 !}

\frac{x + 4}{3} = - 6

\frac{4}{2 - 5 3}

x^{4} - 6 x^{3} + 4 x^{2} + 15 x + 4

98 z^{2} + 39 = 41