What is x/(3x-5)<= 2/(x-1) ?

The solution to x/(3x-5)<= 2/(x-1) is 1<x< 5/3 \lor 2<= x<= 5

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x/(3x-5)<= 2/(x-1)

\frac{x}{3 x - 5} \leq \frac{2}{x - 1}

1 < x < \frac{5}{3} or 2 \leq x \leq 5

Interval Notation

(1, \frac{5}{3}) \cup [2, 5]

Decimal Notation

1 < x < 1.66666 \dots or 2 \leq x \leq 5

Solution steps

\frac{x}{3 x - 5} \leq \frac{2}{x - 1}

Rewrite in standard form

\frac{x ^{2} - 7 x + 10}{( x - 1 ) ( 3 x - 5 )} \leq 0

Factor

\frac{x ^{2} - 7 x + 10}{( x - 1 ) ( 3 x - 5 )} : \frac{( x - 2 ) ( x - 5 )}{( x - 1 ) ( 3 x - 5 )}

\frac{( x - 2 ) ( x - 5 )}{( x - 1 ) ( 3 x - 5 )} \leq 0

Identify the intervals

1 < x < \frac{5}{3} or 2 \leq x \leq 5

0 = 8 x^{2} - 800

\frac{y}{6} - 3 = - 11

2 x - 4 + 5 x - 3 \geq 8

\frac{3}{4} a > - 16

∣ 7 - 2 x ∣ - 2 < - 1

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