Question

What is the solution set of the inequality (4x-3)(2x-1) >0

Answer 1

Hello.

Answer: x<1/2

Step-by-step explanation: Find the critical points of the inequality.

• 8x^2−10x+3=0 (combined)
• (4x−3)(2x−1)=0 (Factor left side of equation)
• 4x−3=0 or 2x−1=0 (Set factors equal to 0)
• X= 1/2

Have a nice day

Answer 2

The solution of the inequality is
`x<(1)/(2)` or
`x>(3)/(4)`

Explanation:

Given : Inequality
`(4x-3)(2x-1) >0`

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.

`(4x-3)(2x-1)=0`

`\text{Either }4x-3=0\text{ or }2x-1=0`

`\text{Either }x=(3)/(4)\text{ or }x=(1)/(2)`

Now, the intervals are

`x<(1)/(2)\\\\(1)/(2)<x<(3)/(4)\\\\x>(3)/(4)`

A test value from each interval into the original inequality to determine which intervals satisfy the inequality.

1)
`x<(1)/(2)`

It is true

2)
`(1)/(2)<x<(3)/(4)`

It is false

3)
`x>(3)/(4)`

It is true

Therefore, The solution of the inequality is
`x<(1)/(2)` or
`x>(3)/(4)`

We can refer the attached figure below to see the solution of inequality shaded one.