Question

the complete solution of the inequation x^2 -4x<12

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Answer 1

The complete solution of the inequation is {x ∈ R : - 2 < x < 6}

Given :

The inequation x² - 4x < 12

To find :

The complete solution of the inequation

Solution :

Step 1 of 2 :

Write down the given inequation

Here the given inequation is

x² - 4x < 12

Step 2 of 2 :

Find complete solution of the inequation

$\displaystyle \sf{ {x}^{2} - 4x < 12 }$

$\displaystyle \sf{ \implies {x}^{2} - 4x - 12 < 0}$

$\displaystyle \sf{ \implies {x}^{2} - (6 - 2)x - 12 < 0}$

$\displaystyle \sf{ \implies {x}^{2} - 6x + 2x - 12 < 0}$

$\displaystyle \sf{ \implies x(x - 6) + 2(x - 6) < 0}$

$\displaystyle \sf{ \implies (x + 2) (x - 6) < 0}$

Above holds only when x > - 2 and x < 6

Combinning we get - 2 < x < 6

Hence the required complete solution of the inequation is {x ∈ R : - 2 < x < 6}

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Learn more from Brainly :-

$1.$ Solve 3x<12=0 when x is a real number and natural number

https://brainly.in/question/13005861

2. Write down the solution set of the inequation x< 6, when the replacement W.

https://brainly.in/question/36657816

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