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

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

Jul 20, 2022

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The solution is (-inf,3/4] U [1/2,inf).

Jul 20, 2022
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See  https://gameshesk14515.web.app/

Guest Jul 20, 2022
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Question: Solve the inequality $$4t^2 \le 9t-2$$

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

$$(4t-1)(t-2) \le 0$$

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.

Jul 21, 2022
edited by Guest  Jul 21, 2022