Hello.
Answer: x<1/2
Step-by-step explanation: Find the critical points of the inequality.
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Answer:
The solution of the inequality is [tex]x<\frac{1}{2}[/tex] or [tex]x>\frac{3}{4}[/tex]
Step-by-step explanation:
Given : Inequality [tex](4x-3)(2x-1) >0[/tex]
To find : The solution set of the inequality?
Solution :
The given inequality is in the factored form,
So, equating it to zero we get the factors.
[tex](4x-3)(2x-1)=0[/tex]
[tex]\text{Either }4x-3=0\text{ or }2x-1=0[/tex]
[tex]\text{Either }x=\frac{3}{4}\text{ or }x=\frac{1}{2}[/tex]
Now, the intervals are
[tex]x<\frac{1}{2}\\\\\frac{1}{2}<x<\frac{3}{4}\\\\x>\frac{3}{4}[/tex]
A test value from each interval into the original inequality to determine which intervals satisfy the inequality.
1) [tex]x<\frac{1}{2}[/tex]
It is true
2) [tex]\frac{1}{2}<x<\frac{3}{4}[/tex]
It is false
3) [tex]x>\frac{3}{4}[/tex]
It is true
Therefore, The solution of the inequality is [tex]x<\frac{1}{2}[/tex] or [tex]x>\frac{3}{4}[/tex]
We can refer the attached figure below to see the solution of inequality shaded one.
