What is |(1-5x)/(2-x)|>4 ?

The solution to |(1-5x)/(2-x)|>4 is x 2

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|(1-5x)/(2-x)|>4

\frac{1 - 5 x}{2 - x} > 4

x < - 7 or 1 < x < 2 or x > 2

Interval Notation

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

Solution steps

\frac{1 - 5 x}{2 - x} > 4

Apply absolute rule: If

∣ u ∣ > a, a > 0

then

u < - a

u > a

\frac{1 - 5 x}{2 - x} < - 4 or \frac{1 - 5 x}{2 - x} > 4

\frac{1 - 5 x}{2 - x} < - 4 or \frac{1 - 5 x}{2 - x} > 4

1 < x < 2 or (x < - 7 or x > 2)

Merge Overlapping Intervals

x < - 7 or 1 < x < 2 or x > 2

\frac{π}{4}

\frac{x}{3} + x = 180

x^{3} + x^{2} - 12

\frac{4}{e ^{2}} \cdot \frac{4}{e ^{2}}

2 π + \frac{π}{2}

What is |(1-5x)/(2-x)|>4 ?
The solution to |(1-5x)/(2-x)|>4 is x<-7\lor 1<x<2\lor x>2