What is the solution set to the inequality (4x-3)(2x-1) greater than 0

(-∞, 1/2) U (3/4, ∞)

Step-by-step explanation:

You need to know for what values of x the first expression is less than zero or greater than zero. You must do the same with the second expression.

To solve the inequality we do the case study.

For the product of (4x-3) (2x-1) to be positive, one of the following cases must occur:

Case I:

(4x-3) < 0 or x < 3/4

          And

(2x-1) < 0 or x < 1/2

Because - * - = +

This is x < 1/2  or  (-∞, 1/2)

It can also happen that:

Case II:

(4x-3) > 0 or x > 3/4

     And

(2x-1) > 0 or x > 1/2

Because + * + = +

This is x > 3/4  or  (3/4, ∞)

Finally the set of solution sought is:

(-∞, 1/2) U (3/4, ∞)

so, converting firstly the mixed fractions to improper fractions and then "adding".