(4x - 3)(2x - 1) ≥ 0
First, find the zeros:
4x - 3 = 0 2x - 1 = 0
x = [tex]\frac{3}{4}[/tex] x = [tex]\frac{1}{2}[/tex]
Next, plot these points and choose test points on the outside and between the zeros:
←-------0------[tex]\frac{1}{2}[/tex]------[tex]\frac{5}{8}[/tex]------[tex]\frac{3}{4}[/tex]------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 [tex]\frac{5}{8}[/tex]: [4([tex]\frac{5}{8}[/tex]) - 3][2([tex]\frac{5}{8}[/tex]) - 1] = ( - )( + ) = - This does NOT work
Test Point 1: [4(1) - 3][2(1) - 1] = ( + )( + ) = + THIS WORKS!
Answer: x ≤ [tex]\frac{1}{2}[/tex] or x ≥ [tex]\frac{3}{4}[/tex]
Interval Notation: (-∞, [tex]\frac{1}{2}[/tex]] U [[tex]\frac{3}{4}[/tex], ∞)
Graph: ←------[tex]\frac{1}{2}[/tex] [tex]\frac{3}{4}[/tex]--------→
