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

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

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

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

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

Interval Notation

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

Decimal Notation

0 < x < 0.5 or x > 2

Solution steps

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

Rewrite in standard form

\frac{- 2 x ^{2} + 4 x}{1 - 2 x} > 0

Factor

\frac{- 2 x ^{2} + 4 x}{1 - 2 x} : \frac{- 2 x ( x - 2 )}{1 - 2 x}

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Divide both sides by

2

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

Simplify

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

Identify the intervals

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

b^{2} + 7 b - 18

- 3 (x - 2) (x + 3)^{2} (x - 11) > 0

9 ∣ 3 n - 2 ∣ + 6 > 51

\frac{x + 5}{3} - \frac{1}{2} x + 3 (2 x - \frac{1}{2}) = 5 (\frac{x}{2} - 2)

24 \cdot 7

What is (1+x)/(1-2x)>1-x ?
The solution to (1+x)/(1-2x)>1-x is 0<x< 1/2 \lor x>2