Question 159123: Use given functions to find all values of x that satisfy the required inequality?
f(x)=4x^2 g(x)=9x-2; f(x)< g(x)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Use given functions to find all values of x that satisfy the required inequality?
f(x)=4x^2 g(x)=9x-2; f(x)< g(x)
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4x^2 < 9x - 2
4x^2 - 9x + 2 < 0
4x^2 -8x -x + 2 < 0
(4x-1)(x-2) < 0
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Find the boundary values: x = 1/4 ; x = 2
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Draw a number line and plot x=1/4 and x = 2
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Check a test value in each resulting interval to see where the solution set is :
Let x= 0; then 4*0^2-9*0+2 < 0; false ; no solutions in (-inf,1/4)
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Let x = 1; then 4*1^2-9*1+2 <0 ; true so solutions in (1/4,2)
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Let x = 3; then 4*3^2 -9*3 + 2 < 0; false so no solutions in (2,+inf)
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Final Solution: (1/4,2)
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Cheers,
Stan H.
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