How do I use a sign chart to solve 2x^2-7x> -32x27x>3?

1 Answer
Apr 4, 2018

Solution: x <0.5 and x>3 or (-oo,0.5)uu(3,oo) x<0.5andx>3or(,0.5)(3,)

Explanation:

2x^2-7x> -3 or 2x^2-7x +3 > 0 2x27x>3or2x27x+3>0 or

2x^2-6x-x +3 > 0 2x26xx+3>0 or

2x(x-3)-1(x -3) > 0 2x(x3)1(x3)>0 or

(x-3)(2x-1) > 0(x3)(2x1)>0

Critical points:

(x-3)(2x-1)=0(x3)(2x1)=0 . Critical points are 2x-1=0:. x= 1/2

and x-3=0:. x= 3:. critical points are 1/2,3

Sign chart:

When x< 1/2 sign of (x-3)(2x-1) is (-) * (-) = (+) ; > 0

When 1/2 < x < 3 sign of (x-3)(2x-1) is (-) * (+) = (-) ; < 0

When x> 3 sign of (x-3)(2x-1) is (+) * (+) = (+) ; > 0

Solution: x <0.5 and x>3 or (-oo,0.5)uu(3,oo) [Ans]