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

The solution to ((2x-3))/((3x-5))>= 3 is 5/3 <x<= 12/7

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

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

\frac{5}{3} < x \leq \frac{12}{7}

Interval Notation

(\frac{5}{3}, \frac{12}{7}]

Decimal Notation

1.66666 \dots < x \leq 1.71428 \dots

Solution steps

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

Rewrite in standard form

\frac{- 7 x + 12}{3 x - 5} \geq 0

Identify the intervals

\frac{5}{3} < x \leq \frac{12}{7}

x^{2} - 3 x + 4 > 0

\frac{( x + 2 )}{( x - 1 )} < 4

\frac{( 7 - 2 k )}{( 4 ( - k ) )} \leq 1

\frac{( 2 ( x - 4 ) )}{( ( x - 1 ) ( x - 7 ) )} \leq \frac{1}{( x - 2 )}

(x - 1) (x - 2) \cdot (x - 3)^{2} > 0

What is ((2x-3))/((3x-5))>= 3 ?
The solution to ((2x-3))/((3x-5))>= 3 is 5/3 <x<= 12/7