Answer:
x <= 1/2 or x >= 3/4
In interval notation:
[tex] (-\infty, \dfrac{1}{2}] \land [\dfrac{3}{4}, \infty) [/tex]
Step-by-step explanation:
First, solve the related equation for x.
(4x - 3)(2x - 1) = 0
4x - 3 = 0 or 2x - 1 = 0
4x = 3 or 2x = 1
x = 3/4 or x = 1/2
Now you have 2 points of interest, 1/2 and 3/4.
Plot these two numbers on a number line using solid dots.
The number line is now divided into three regions: left of 1/2, between 1/2 and 3/4, and right of 3/4. We need to test a point from each region to see which regions are part of the solution.
Test -1
(4x - 3)(2x - 1) => 0
[4(-1) - 3][2(-1) - 1] => 0 ?
(-7)(-3) => 0 ?
21 => 0 True
The interval left of 1/2 up to and including 1/2 is part of the solution.
Test 0.6
(4x - 3)(2x - 1) => 0
[4(0.6) - 3][2(0.6) - 1) => 0 ?
(-0.6)(0.2) => 0 ?
-0.12 => 0 False
The interval between 1/2 and 3/4 is not part of the solution.
Test 1
(4x - 3)(2x - 1) => 0
[4(1) - 3][2(1) - 1] => 0 ?
(1)(1) => 0 ?
1 => 0 True
The interval right of 1/2 including 1/2 is part of the solution.
Answer:
x <= 1/2 or x >= 3/4
In interval notation:
[tex] (-\infty, \dfrac{1}{2}] \land[\dfrac{3}{4}, \infty) [/tex]
