What is |(3x+5)/(2-5x)|>= 2 ?

The solution to |(3x+5)/(2-5x)|>= 2 is -1/13 <= x< 2/5 \lor 2/5 <x<= 9/7

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|(3x+5)/(2-5x)|>= 2

\frac{3 x + 5}{2 - 5 x} \geq 2

- \frac{1}{13} \leq x < \frac{2}{5} or \frac{2}{5} < x \leq \frac{9}{7}

Interval Notation

[- \frac{1}{13}, \frac{2}{5}) \cup (\frac{2}{5}, \frac{9}{7}]

Decimal Notation

- 0.07692 \dots \leq x < 0.4 or 0.4 < x \leq 1.28571 \dots

Solution steps

\frac{3 x + 5}{2 - 5 x} \geq 2

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

u \geq a

\frac{3 x + 5}{2 - 5 x} \leq - 2 or \frac{3 x + 5}{2 - 5 x} \geq 2

\frac{3 x + 5}{2 - 5 x} \leq - 2 or \frac{3 x + 5}{2 - 5 x} \geq 2

- \frac{1}{13} \leq x < \frac{2}{5} or \frac{2}{5} < x \leq \frac{9}{7}

\frac{4 2}{3 5}

- 5 x - 6 \geq 9

x^{2} + (10 - 2 x)^{2} = 25

2.02 x + 4.8 = 14.782 - 1.2 x

- \frac{r}{3} = - 7

What is |(3x+5)/(2-5x)|>= 2 ?
The solution to |(3x+5)/(2-5x)|>= 2 is -1/13 <= x< 2/5 \lor 2/5 <x<= 9/7