What is 10>|(x-2)/2 |>4 ?

The solution to 10>|(x-2)/2 |>4 is -18<x<-6\lor 10<x<22

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10>|(x-2)/2 |>4

10 > \frac{x - 2}{2} > 4

- 18 < x < - 6 or 10 < x < 22

Interval Notation

(- 18, - 6) \cup (10, 22)

Solution steps

10 > \frac{x - 2}{2} > 4

a > u > b

then

a > u and u > b

10 > \frac{x - 2}{2} and \frac{x - 2}{2} > 4

10 > \frac{x - 2}{2} : - 18 < x < 22

\frac{x - 2}{2} > 4 : x < - 6 or x > 10

Combine the intervals

- 18 < x < 22 and (x < - 6 or x > 10)

Merge Overlapping Intervals

- 18 < x < - 6 or 10 < x < 22

5 x (x - 2) + 7 = 0

3 (x - 3)^{2} + 12 = 0

8 x^{2} - 28 x - 16

2 x \cdot 4 x^{- \frac{5}{2}}

What is 10>|(x-2)/2 |>4 ?
The solution to 10>|(x-2)/2 |>4 is -18<x<-6\lor 10<x<22