Question

For what x is 3x+3>4xx−2?

Answer 1

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= 3x + 3 > 4x - 2

= 3 + 2 > 4x - 3x

= 5 > x

= x < 5

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Answer 2

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3x + 3 > 4x² - 2

=>

Subtract both sides -4x²

-4x² + 3x + 3 > -2

Add both sides +2

-4x² + 3x + 3 + 2 > 0

-4x² + 3x + 5 > 0

Multiply both sides by -

4x² - 3x - 5 < 0

Divide both sides by 4

x² -3x/4 -5/4 < 0

x² - 2 ( x ) ( 3/8 ) + 9/64 - 9/64 - 5/4 <0

( x - 3/8 )² < 54/64

( x - 3/8 )² < 27/32

±( x - 3/8 ) < 3√3/4√2

( x - 3/8 ) < 3√3/4√2

OR.

-( x - 3/8 )< 3√3/4√2

=>

x < ( 3√6 + 3 )/8

And

x > - ( 3√6 + 3) /8