Question

Which is the solution set to the inequality (4x-3)(2x-1)&gt=0?

Answer 1

(4x - 3)(2x - 1) ≥ 0

First, find the zeros:

4x - 3 = 0 2x - 1 = 0

x =
`(3)/(4)` x =
`(1)/(2)`

Next, plot these points and choose test points on the outside and between the zeros:

←-------0------
`(1)/(2)`------
`(5)/(8)`------
`(3)/(4)`------1------→

Lastly, plug in the test points and look for a positive result (since it is greater than 0).

Test Point 0: [4(0) - 3][2(0) - 1] = ( - )( - ) = + THIS WORKS!

Test Point
`(5)/(8)`: [4(
`(5)/(8)`) - 3][2(
`(5)/(8)`) - 1] = ( - )( + ) = - This does NOT work

Test Point 1: [4(1) - 3][2(1) - 1] = ( + )( + ) = + THIS WORKS!

Answer: x ≤
`(1)/(2)` or x ≥
`(3)/(4)`

Interval Notation: (-∞,
`(1)/(2)`] U [
`(3)/(4)`, ∞)

Graph: ←------
`(1)/(2)`
`(3)/(4)`--------→