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

The solution to |((x+2))/((3x-5))|>= 5 is 23/16 <= x< 5/3 \lor 5/3 <x<= 27/14

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

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

\frac{23}{16} \leq x < \frac{5}{3} or \frac{5}{3} < x \leq \frac{27}{14}

Interval Notation

[\frac{23}{16}, \frac{5}{3}) \cup (\frac{5}{3}, \frac{27}{14}]

Decimal Notation

1.4375 \leq x < 1.66666 \dots or 1.66666 \dots < x \leq 1.92857 \dots

Solution steps

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

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

u \geq a

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

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

\frac{23}{16} \leq x < \frac{5}{3} or \frac{5}{3} < x \leq \frac{27}{14}

[\frac{n}{( 2 - 3 )}] - 1 < \frac{1}{10}

∣ x - 1 ∣ > ∣ x - 2 ∣

∣ 4 x - 5 ∣ < 8

∣ 2 x + 1 ∣ + ∣ 2 x - 1 ∣ > 5

\frac{( x - 4 )}{( x ^{2} - 36 )} \leq 0

What is |((x+2))/((3x-5))|>= 5 ?
The solution to |((x+2))/((3x-5))|>= 5 is 23/16 <= x< 5/3 \lor 5/3 <x<= 27/14