Question

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

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

x <= 1/2 or x >= 3/4

In interval notation:

$(-\infty, \dfrac{1}{2}] \land [\dfrac{3}{4}, \infty)$

Step-by-step explanation:

First, solve the related equation for x.

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

4x - 3 = 0 or 2x - 1 = 0

4x = 3 or 2x = 1

x = 3/4 or x = 1/2

Now you have 2 points of interest, 1/2 and 3/4.

Plot these two numbers on a number line using solid dots.

The number line is now divided into three regions: left of 1/2, between 1/2 and 3/4, and right of 3/4. We need to test a point from each region to see which regions are part of the solution.

Test -1

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

[4(-1) - 3][2(-1) - 1] => 0 ?

(-7)(-3) => 0 ?

21 => 0 True

The interval left of 1/2 up to and including 1/2 is part of the solution.

Test 0.6

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

[4(0.6) - 3][2(0.6) - 1) => 0 ?

(-0.6)(0.2) => 0 ?

-0.12 => 0 False

The interval between 1/2 and 3/4 is not part of the solution.

Test 1

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

[4(1) - 3][2(1) - 1] => 0 ?

(1)(1) => 0 ?

1 => 0 True

The interval right of 1/2 including 1/2 is part of the solution.

Answer:

x <= 1/2 or x >= 3/4

In interval notation:

$(-\infty, \dfrac{1}{2}] \land[\dfrac{3}{4}, \infty)$