Question

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

Answer 1

$6x^2-x$

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

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

In interval notation, the solution set is

$\boxed{-\dfrac12$