What is | 5/(2x-1)|>= | 1/(x-2)| ?

The solution to | 5/(2x-1)|>= | 1/(x-2)| is x = 3

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| 5/(2x-1)|>= | 1/(x-2)|

\frac{5}{2 x - 1} \geq \frac{1}{x - 2}

x < \frac{1}{2} or \frac{1}{2} < x \leq \frac{11}{7} or x \geq 3

Interval Notation

(- \infty, \frac{1}{2}) \cup (\frac{1}{2}, \frac{11}{7}] \cup [3, \infty)

Decimal Notation

x < 0.5 or 0.5 < x \leq 1.57142 \dots or x \geq 3

Solution steps

\frac{5}{2 x - 1} \geq \frac{1}{x - 2}

Find positive and negative intervals

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

Solve the inequality for each interval

x < \frac{1}{2} or \frac{1}{2} < x \leq \frac{11}{7} or x \geq 3

8 = x^{2} - 4

4 x^{4} + 7 x^{2} - 2 = 0

- 4 (2 x - 6) = 10 x

10 m^{3} + 4 m^{2} - 90 m - 36

4 m^{2} - 4 mn + n^{2}

What is | 5/(2x-1)|>= | 1/(x-2)| ?
The solution to | 5/(2x-1)|>= | 1/(x-2)| is x< 1/2 \lor 1/2 <x<= 11/7 \lor x>= 3