What is ((2(x-4)))/(((x-1)(x-7)))>= 1/((x-2)) ?

The solution to ((2(x-4)))/(((x-1)(x-7)))>= 1/((x-2)) is 1 7

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((2(x-4)))/(((x-1)(x-7)))>= 1/((x-2))

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

1 < x < 2 or x > 7

Interval Notation

(1, 2) \cup (7, \infty)

Solution steps

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

Rewrite in standard form

\frac{x ^{2} - 4 x + 9}{( x - 1 ) ( x - 7 ) ( x - 2 )} \geq 0

Identify the intervals

1 < x < 2 or x > 7

- 3 m^{2} + 2 m + 1 \leq 0

\frac{- 1}{( x + 3 )} > 0

n^{2} < n

\frac{1 - 1}{x ^{2}} > 0

(x - 11) \cdot (x^{2} - 7 x + 10) > 0

What is ((2(x-4)))/(((x-1)(x-7)))>= 1/((x-2)) ?
The solution to ((2(x-4)))/(((x-1)(x-7)))>= 1/((x-2)) is 1<x<2\lor x>7