Which of the following represents the solution of the inequality(4x - 3)(1 - x) > 0?

To solve the inequality (4x - 3)(1 - x) > 0, follow these steps:

Step 1: Set each factor equal to zero and solve for x. This will give you the critical points of the inequality.

4x - 3 = 0 4x = 3 x = 3/4

1 - x = 0 x = 1

Step 2: The critical points divide the number line into intervals. Test each interval to see if it makes the inequality true.

Test x < 3/4: Choose x = 0. Then (4*0 - 3)(1 - 0) = -3 > 0, which is false.

Test 3/4 < x < 1: Choose x = 0.8. Then (4*0.8 - 3)(1 - 0.8) = 0.2 > 0, which is true.

Test x > 1: Choose x = 2. Then (4*2 - 3)(1 - 2) = -3 > 0, which is false.

Step 3: The solution to the inequality is the interval where the inequality is true, so the solution is 3/4 < x < 1.