What is (30}{x-1}-\frac{30)/x >= 1 ?

The solution to (30}{x-1}-\frac{30)/x >= 1 is -5<= x<0\lor 1<x<= 6

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(30}{x-1}-\frac{30)/x >= 1

\frac{30}{x - 1} - \frac{30}{x} \geq 1

- 5 \leq x < 0 or 1 < x \leq 6

Interval Notation

[- 5, 0) \cup (1, 6]

Solution steps

\frac{30}{x - 1} - \frac{30}{x} \geq 1

Rewrite in standard form

\frac{- x ^{2} + x + 30}{x ( x - 1 )} \geq 0

Factor

\frac{- x ^{2} + x + 30}{x ( x - 1 )} : \frac{- ( x + 5 ) ( x - 6 )}{x ( x - 1 )}

\frac{- ( x + 5 ) ( x - 6 )}{x ( x - 1 )} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x + 5 ) ( x - 6 ) ) ( - 1 )}{x ( x - 1 )} \leq 0 \cdot (- 1)

Simplify

\frac{( x + 5 ) ( x - 6 )}{x ( x - 1 )} \leq 0

Identify the intervals

- 5 \leq x < 0 or 1 < x \leq 6

3 x^{2} - 30 x + 72

- \frac{\frac{2}{3}}{- \frac{2}{3}}

2 b^{2} + 5 b - 12

\frac{10}{3} = \frac{x}{- \frac{5}{2}}

5 x^{2} - 4 x - 1 \leq 0

What is (30}{x-1}-\frac{30)/x >= 1 ?
The solution to (30}{x-1}-\frac{30)/x >= 1 is -5<= x<0\lor 1<x<= 6