What is 1/(1-x)>1-2x ?

The solution to 1/(1-x)>1-2x is 0 3/2

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1/(1-x)>1-2x

\frac{1}{1 - x} > 1 - 2 x

0 < x < 1 or x > \frac{3}{2}

Interval Notation

(0, 1) \cup (\frac{3}{2}, \infty)

Decimal

0 < x < 1 or x > 1.5

Solution steps

\frac{1}{1 - x} > 1 - 2 x

Rewrite in standard form

\frac{- 2 x ^{2} + 3 x}{1 - x} > 0

Factor

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

\frac{- x ( 2 x - 3 )}{1 - x} > 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - x ( 2 x - 3 ) ) ( - 1 )}{1 - x} < 0 \cdot (- 1)

Simplify

\frac{x ( 2 x - 3 )}{1 - x} < 0

Identify the intervals

0 < x < 1 or x > \frac{3}{2}

x^{2} - 5 x - 66 = 0

109 = \frac{( 9 \cdot 1 0 ^{9} ) \cdot q}{( 6.38 \cdot 1 0 ^{6} ) ^{2}}

16.1

12 \cdot 2

\frac{7}{10} + \frac{2}{15}