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

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

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

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

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

Solution steps

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

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

u \geq a

\frac{1 - x}{2 x + 1} \leq - 1 or \frac{1 - x}{2 x + 1} \geq 1

\frac{1 - x}{2 x + 1} \leq - 1 or \frac{1 - x}{2 x + 1} \geq 1

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

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

x^{3} + 4 x^{2} - 5 x

6 (x + 6)^{2} (2 x - 5)^{2} - (x + 6) (2 x - 5)^{3}

- - 14

3 x^{2} - 6 x - 24 = 0

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