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Solve the inequality 4t^2 \le -9t + 12 - 4t + 23 + (2t - 1)(2t + 1). Write your answer in interval notation.

 Aug 10, 2024
 #1
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First, let's simplify the right hand side of the equation a little bit. 

We get that \(-9t+12-4t+23+4t^2-1=-13t+4t^2+34\)

 

Now, we simply move all terms to one side. Note that most terms cancel out. 

we get the equation

\(13t-34\le \:0\)

 

Solving for t, we get

\(13t\le \:34\\t\le \:\frac{34}{13}\)

 

In interval notation, this is

\((-inf, \frac{34}{13}]\)

 

Thanks! :)

 Aug 10, 2024
edited by NotThatSmart  Aug 10, 2024

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