+130536 6x^2 - x < 2 subtract 2 from both sides
6x^2 - x - 2 < 0 factor the left side
(2x + 1) (3x - 2) < 0 (1)
Set both of the linear factors to 0 and solve for x
2x + 1 = 0 3x - 2 = 0
2x = -1 3x = 2
x = -1/2 x = 2/3
We have three possible intervals to test
(-inf, -1/2) ( -1/2, 2/3) (2/3, inf)
Either the first and third intervals solve (1) or the middle interval does
Pick an x value on ( -1/2, 2/3) [ I'll choose x = 0 ] and note that
(2(0) + 1) ( 3(0) -2) < 2 ????
(1) ( -2) = < 2 ???
-2 < 2 is true
So.....the interval (-1/2, 2/3) is the solution....
+1253 Another way of doing it...
You can find the x-intercepts by setting the equation to \(6x^2-x-2=0\), and \(x=-\frac{1}{2}, \frac{2}{3}\).
Since the equation is saying that \(6x^2-x-2<0,\) all values below the x-axis are answers, and therefore, the answer is
\((-\frac{1}{2}, \frac{2}{3})\).
You are very welcome!
:P
