Respuesta :
The given question is wrong.
Question:
What is the solution set to the inequality (4x – 3) (2x – 1) ≥ 0?
(A) [tex]\{x| x\leq 3\ \text {or} \ x\geq 1[/tex]
(B) [tex]\{x| x\leq 2\ \text {or} \ x\geq \frac{4}{3}[/tex]
(C) [tex]\{x| x\leq \frac{1}{2}\ \text {or} \ x\geq \frac{3}{4}[/tex]
(D) [tex]\{x| x\leq \frac{-1}{2}\ \text {or} \ x\geq \frac{-3}{4}[/tex]
Answer:
The solution set to the given inequality is [tex]\{x| x\leq \frac{1}{2}\ \text {or} \ x\geq \frac{3}{4}[/tex].
Solution:
Given expression is (4x – 3) (2x – 1) ≥ 0.
Let us take the expression is equal to zero.
(4x – 3) (2x – 1) = 0
By quadratic factor, If AB = 0, then A = 0 or B = 0.
(4x – 3) = 0 or (2x – 1) = 0
Let us take the first factor equal to zero.
⇒ 4x – 3 = 0
⇒ 4x = 3
[tex]$x=\frac{3}{4}[/tex]
Now, take the second factor equal to zero.
⇒ 2x – 1 = 0
⇒ 2x = 1
[tex]$x=\frac{1}{2}[/tex]
So, [tex]$x=\frac{1}{2},x=\frac{3}{4}[/tex].
Now, write it in the inequality to make the statement true.
[tex]$x\geq \frac{1}{2}\ \text{(or)}\ x\leq \frac{3}{4}[/tex]
Option C is the correct answer.
The solution set to the given inequality is [tex]\{x| x\leq \frac{1}{2}\ \text {or} \ x\geq \frac{3}{4}[/tex].
