What is |x|>= |2x-1| ?

The solution to |x|>= |2x-1| is 1/3 <= x<= 1

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|x|>= |2x-1|

∣ x ∣ \geq ∣ 2 x - 1 ∣

\frac{1}{3} \leq x \leq 1

Solution steps

∣ x ∣ \geq ∣ 2 x - 1 ∣

Find positive and negative intervals

x < 0, 0 \leq x < \frac{1}{2}, x \geq \frac{1}{2}

Solve the inequality for each interval

No Solution or \frac{1}{3} \leq x < \frac{1}{2} or \frac{1}{2} \leq x \leq 1

Merge Overlapping Intervals

\frac{1}{3} \leq x \leq 1

s^{2} - 3 s + 2 = 0

(\frac{x ^{7} y ^{3}}{x})^{\frac{1}{3}}

3^{16}

- 9 x + 2 > 18

\frac{1}{6} (- 9)