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

User BDarley
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2 Answers

2 votes

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



User Gebi
by
6.6k points
3 votes

Answer:

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.

What is the solution set of the inequality (4x-3)(2x-1) >0-example-1
User Lucas Pacheco
by
6.5k points