SOLUTION: Question: Solve: {{{6x^2+5x<4}}} How do i solve this? Do i need a chart?

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Question 92719: Question: Solve: 6x%5E2%2B5x%3C4
How do i solve this? Do i need a chart?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
find the roots of the equality 6x^2+5x=4 ... 6x^2+5x-4=0 ... factoring gives (3x+4)(2x-1)=0 ... so the roots are -3/4 and 1/2

the roots are the "boundry points" between solutions ... in this case, the three ranges are <-3/4, between -3/4 and 1/2, and >1/2

test a range by choosing a value in it ... 0 is between -3/4 and 1/2 ... 6(0^2)+5(0)<4 ... 0<4 so x must be between -3/4 and 1/2

testing the other ranges will show no solution; this is because the "boundry points" are between solutions and non-solutions

(-3/4) < x < (1/2)