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

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

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

\frac{∣ x + 1 ∣}{∣ 1 - 2 x ∣} \geq 1

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

Interval Notation

[0, \frac{1}{2}) \cup (\frac{1}{2}, 2]

Decimal Notation

0 \leq x < 0.5 or 0.5 < x \leq 2

Solution steps

\frac{∣ x + 1 ∣}{∣ 1 - 2 x ∣} \geq 1

Find positive and negative intervals

x < - 1, - 1 \leq x \leq \frac{1}{2}, x > \frac{1}{2}

Solve the inequality for each interval

No Solution or 0 \leq x < \frac{1}{2} or \frac{1}{2} < x \leq 2

Merge Overlapping Intervals

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

x^{\frac{3}{2}} - 8 x^{\frac{1}{2}}

3 x^{2} - 24 x + 50 = 0

\frac{12 x ^{8} y ^{6}}{18 x ^{4} y ^{3}}

- 3 (u + 5) + 2 = 4 (u + 2)

∣ y - 2 ∣ > 9

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