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

Answer:

The solution of the inequality is $x$ or $x>\frac{3}{4}$

Step-by-step 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.

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

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

$\text{Either }x=\frac{3}{4}\text{ or }x=\frac{1}{2}$

Now, the intervals are

$x$

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

1) $x$

It is true

2)  $\frac{1}{2}$

It is false

3) $x>\frac{3}{4}$

It is true

Therefore, The solution of the inequality is $x$ or $x>\frac{3}{4}$

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