What is (56}{x-1}-\frac{56)/x >= 1 ?

The solution to (56}{x-1}-\frac{56)/x >= 1 is -7<= x<0\lor 1<x<= 8

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(56}{x-1}-\frac{56)/x >= 1

\frac{56}{x - 1} - \frac{56}{x} \geq 1

- 7 \leq x < 0 or 1 < x \leq 8

Interval Notation

[- 7, 0) \cup (1, 8]

Solution steps

\frac{56}{x - 1} - \frac{56}{x} \geq 1

Rewrite in standard form

\frac{- x ^{2} + x + 56}{x ( x - 1 )} \geq 0

Factor

\frac{- x ^{2} + x + 56}{x ( x - 1 )} : \frac{- ( x + 7 ) ( x - 8 )}{x ( x - 1 )}

\frac{- ( x + 7 ) ( x - 8 )}{x ( x - 1 )} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x + 7 ) ( x - 8 ) ) ( - 1 )}{x ( x - 1 )} \leq 0 \cdot (- 1)

Simplify

\frac{( x + 7 ) ( x - 8 )}{x ( x - 1 )} \leq 0

Identify the intervals

- 7 \leq x < 0 or 1 < x \leq 8

5 n^{2} - 4 n - 10 = 15

∣ x - 1 ∣ \leq 3

x^{2} > - 2 x

4 x^{2} - 1

3 x^{3} + 14 x^{2} - 5 x

What is (56}{x-1}-\frac{56)/x >= 1 ?
The solution to (56}{x-1}-\frac{56)/x >= 1 is -7<= x<0\lor 1<x<= 8