Answer
(-infinity, $-2/3$) U $(3/2$, infinity)
Work Step by Step
$6x^2-5x\geq6$
$6x^2-5x-6\geq 0$
$6x^2-5x-6=0$
$6x^2-9x+4x-6=0$
$3x(2x-3)+2(2x-3)=0$
$(2x-3)(3x+2)=0$
$2x-3=0$
$2x=3$
$2x/2=3/2$
$x=3/2$
$3x+2=0$
$3x=-2$
$3x/3=-2/3$
$x=-2/3$
(-infinity, $-2/3$)
$(-2/3, 3/2)$
$(3/2$, infinity)
Let $x=-1$, $x=0$, $x=3$
$x=-1$
$6x^2-5x\geq6$
$6(-1)^2-5(-1)\geq6$
$6*1+5\geq 6$
$6+5\geq 6$
$11 \geq 6$ (true)
$x=0$
$6x^2-5x\geq6$
$6*0^2-5*0\geq6$
$6*0-0\geq 6$
$0-0\geq 6$
$0\geq 6$ (false)
$x=3$
$6x^2-5x\geq6$
$6*3^2-5*3\geq6$
$6*9-15\geq 6$
$54-15\geq 6$
$36 \geq 6$ (true)
