What is (11)/((5x-4))-(10)/((4-5x))>= 1 ?

The solution to (11)/((5x-4))-(10)/((4-5x))>= 1 is 4/5 <x<= 5

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(11)/((5x-4))-(10)/((4-5x))>= 1

\frac{11}{( 5 x - 4 )} - \frac{10}{( 4 - 5 x )} \geq 1

\frac{4}{5} < x \leq 5

Interval Notation

(\frac{4}{5}, 5]

Decimal Notation

0.8 < x \leq 5

Solution steps

\frac{11}{5 x - 4} - \frac{10}{4 - 5 x} \geq 1

Rewrite in standard form

\frac{25 x ^{2} - 145 x + 100}{( 5 x - 4 ) ( - 5 x + 4 )} \geq 0

Factor

\frac{25 x ^{2} - 145 x + 100}{( 5 x - 4 ) ( - 5 x + 4 )} : \frac{5 ( 5 x - 4 ) ( x - 5 )}{( 5 x - 4 ) ( - 5 x + 4 )}

\frac{5 ( 5 x - 4 ) ( x - 5 )}{( 5 x - 4 ) ( - 5 x + 4 )} \geq 0

Divide both sides by

5

\frac{\frac{5 ( 5 x - 4 ) ( x - 5 )}{( 5 x - 4 ) ( - 5 x + 4 )}}{5} \geq \frac{0}{5}

Simplify

\frac{x - 5}{- 5 x + 4} \geq 0

Identify the intervals

\frac{4}{5} < x \leq 5

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x^{2} - 2 > 7

- x^{2} + 2 x > \frac{4 x - 1}{4}

(2 x - 1) (x^{2} - x - 6) < 0

x^{3} - 48 \leq 4 x (3 x - 11)

What is (11)/((5x-4))-(10)/((4-5x))>= 1 ?
The solution to (11)/((5x-4))-(10)/((4-5x))>= 1 is 4/5 <x<= 5