+1055 Solve the inequality 4t^2 \le -9t + 12 - 4t + 23 + (2t - 1)(2t + 1). Write your answer in interval notation.
+1804 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! :)
