Question

6x^2-x<2 solve, show your answer on a number line. State your answer in interval notation

Answer 1

`6x^2-x<2\implies6x^2-x-2<0\implies(3x-2)(2x+1)<0`

In order for the left side to be negative, we need either
`3x-2>0` and
`2x+1<0`, or
`3x-2<0` and
`2x+1>0`.

• If
  `3x-2>0` and
  `2x+1<0`, then
  `x>\frac23` and
  `x<-\frac12`. There is no value of
  `x` that meets both conditions, so this case offers no solutions.
• If
  `3x-2<0` and
  `2x+1>0`, then
  `x<\frac23` and
  `x>-\frac12`. This means any number
  `x` between -1/2 and 2/3 satisfies the inequality.

In interval notation, the solution set is

`\boxed{-\frac12<x<\frac23}`