What is 2/(|2x-3|)>= 3 ?

The solution to 2/(|2x-3|)>= 3 is 7/6 <= x< 3/2 \lor 3/2 <x<= 11/6

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2/(|2x-3|)>= 3

\frac{2}{∣ 2 x - 3 ∣} \geq 3

\frac{7}{6} \leq x < \frac{3}{2} or \frac{3}{2} < x \leq \frac{11}{6}

Interval Notation

[\frac{7}{6}, \frac{3}{2}) \cup (\frac{3}{2}, \frac{11}{6}]

Decimal Notation

1.16666 \dots \leq x < 1.5 or 1.5 < x \leq 1.83333 \dots

Solution steps

\frac{2}{∣ 2 x - 3 ∣} \geq 3

Find positive and negative intervals

x < \frac{3}{2}, x \geq \frac{3}{2}

Solve the inequality for each interval

\frac{7}{6} \leq x < \frac{3}{2} or \frac{3}{2} < x \leq \frac{11}{6}

- 10 x + 9 \leq - 9 (x - 1)

2 x - 10 \geq 8

(x + 1)^{2} (x - 1)^{2}

\frac{a}{2} + \frac{a}{3}

\frac{x + 3}{2} + \frac{x + 5}{5} = 8

What is 2/(|2x-3|)>= 3 ?
The solution to 2/(|2x-3|)>= 3 is 7/6 <= x< 3/2 \lor 3/2 <x<= 11/6