Solve the following inequalities algebraically. Express the answer in interval notation and graph the solution set on a number line.
6x^2-5x-4<0
solve as you would a quadratic:
we have: $\displaystyle (3x - 4)(2x + 1) < 0$
so, $\displaystyle x < \frac 43$ or $\displaystyle x < - \frac 12$
but the inequality signs are often misleading in this case, so we must check our solutions.
thus the solution lies in one or some union of the following intervals (we cut the real line into pieces defined by our solution):
$\displaystyle \left(- \infty, - \frac 12 \right)$, $\displaystyle \left( - \frac 12, \frac 43 \right)$ and $\displaystyle \left( \frac 43, \infty \right)$
now check which work in the original inequality by picking any number in each interval and plugging them in for x to see if it makes sense