Solve the inequality $4t^2 \le 9t - 2.$

Question: Solve the inequality $4t^2 \le 9t-2$

We rearrange it as follows:
$4t^2-9t+2 \le 0$

Then, factor this quadratic equation:
$(4t-1)(t-2) \le 0$

The critical values (also called endpoints) are: $t_1=\frac{1}{4},t_2=2$

So, if we sketched the quadratic $4t^2-9t+2$, it has x-intercepts (1/4 and 2).

And we want the region below the x-axis (As it is less than 0).

Hence, the region between 1/4 and 2.

Therefore: $\frac{1}{4} \le t \le 2$

Here is a sketch: (Using desmos.com)

I hope this helps.