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 = $\frac{3}{4}$               x = $\frac{1}{2}$

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

←-------0------$\frac{1}{2}$------$\frac{5}{8}$------$\frac{3}{4}$------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 $\frac{5}{8}$: [4($\frac{5}{8}$) - 3][2($\frac{5}{8}$) - 1]  = ( - )( + ) = -  This does NOT work

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

Answer: x ≤ $\frac{1}{2}$   or   x ≥ $\frac{3}{4}$

Interval Notation: (-∞, $\frac{1}{2}$] U [$\frac{3}{4}$, ∞)

Graph: ←------$\frac{1}{2}$          $\frac{3}{4}$--------→