What is |-7/x+10|>= 12(x-1) ?

The solution to |-7/x+10|>= 12(x-1) is x<0\lor 0<x<= (11+sqrt(37))/(12)

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|-7/x+10|>= 12(x-1)

- \frac{7}{x} + 10 \geq 12 (x - 1)

x < 0 or 0 < x \leq \frac{11 + 37}{12}

Interval Notation

(- \infty, 0) \cup (0, \frac{11 + 37}{12}]

Decimal Notation

x < 0 or 0 < x \leq 1.42356 \dots

Solution steps

- \frac{7}{x} + 10 \geq 12 (x - 1)

Find positive and negative intervals

x < 0, 0 \leq x < \frac{7}{10}, x \geq \frac{7}{10}

Solve the inequality for each interval

x < 0 or 0 < x < \frac{7}{10} or \frac{7}{10} \leq x \leq \frac{11 + 37}{12}

Merge Overlapping Intervals

x < 0 or 0 < x \leq \frac{11 + 37}{12}

\frac{( x - y )}{( x + 2 y )}

x^{3} + 7 x^{2} - 5 x - 35

x - 12 \geq 8

(- 4)^{\frac{2}{3}}

17 x = 204

What is |-7/x+10|>= 12(x-1) ?
The solution to |-7/x+10|>= 12(x-1) is x<0\lor 0<x<= (11+sqrt(37))/(12)