Solve `(x-1)(x-2)(1-2x)> 0.`

Explanation

We have `(x-1)(x-2)(1-2x) gt 0`
or` -(x-1)(x-2)(2x-1) gt 0`
or `(x-1)(x-2)(2x-1) lt 0`
On the number line, mark `x=1//2,1,2`

When `x gt 2,` all factors `(x-1),(2x-1),` and `(x-2)` are passive.
Hence, `(x-1)(x-2)(2x-1) gt 0 ` for `x gt 2`.
Now put positive and negative signs alternatively as shown in the figure.
Hence, solution set of `(x-1)(x-2)(1-2x) gt 0` or `(x-1)(x-2)(2x-1) lt 0 " is " (-oo,1//2) cup (1,2).`