What is x-2<x(x-4)<5 ?

The solution to x-2<x(x-4)<5 is -1<x<(-sqrt(17)+5)/2 \lor (sqrt(17)+5)/2 <x<5

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x-2<x(x-4)<5

x - 2 < x (x - 4) < 5

- 1 < x < \frac{- 17 + 5}{2} or \frac{17 + 5}{2} < x < 5

Interval Notation

(- 1, \frac{- 17 + 5}{2}) \cup (\frac{17 + 5}{2}, 5)

Decimal Notation

- 1 < x < 0.43844 \dots or 4.56155 \dots < x < 5

Solution steps

x - 2 < x (x - 4) < 5

a < u < b

then

a < u and u < b

x - 2 < x (x - 4) and x (x - 4) < 5

x - 2 < x (x - 4) : x < \frac{- 17 + 5}{2} or x > \frac{17 + 5}{2}

x (x - 4) < 5 : - 1 < x < 5

Combine the intervals

(x < \frac{- 17 + 5}{2} or x > \frac{17 + 5}{2}) and - 1 < x < 5

Merge Overlapping Intervals

- 1 < x < \frac{- 17 + 5}{2} or \frac{17 + 5}{2} < x < 5

x + 8 < 0 or 3 x > - 18

0.04 > 0.1

x^{2} - 16 x + 113 = 0

10 y^{3} + 5 y

\frac{x - 1}{2} < 4

What is x-2<x(x-4)<5 ?
The solution to x-2<x(x-4)<5 is -1<x<(-sqrt(17)+5)/2 \lor (sqrt(17)+5)/2 <x<5