The solution set to the inequality -2x^2 + 8x - 6 > 0 is ?

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Answer 1 · 2018-07-22T13:19:52

#x\in(1, 3)#

#-2x^2+8x-6>0#

#-2(x^2-4x+3)>0#

#\frac{-2(x^2-4x+3)}{-2}<\frac{0}{-2}#

#x^2-4x+3<0#

#x^2-3x-x+3<0#

#x(x-3)-(x-3)<0#

#(x-3)(x-1)<0#

setting #x-3=0\implies x=3# &

#x-1=0\implies x=1#

Specifying #x=3# & #x=1# on the number lines & dividing it in positive & negative intervals we get the desired solution

#x\in(1, 3)#