To solve the given inequality \( -1.9x^2 + 3.75 > 2.11 \), we can follow these steps:
First, we can subtract 2.11 from both sides of the inequality:
\( -1.9x^2 + 3.75 - 2.11 > 0 \)
Simplify the left side:
\( -1.9x^2 + 1.64 > 0 \)
Now, to isolate the quadratic term, we can divide the entire inequality by -1.9, remembering to reverse the inequality sign when dividing by a negative value:
\( x^2 - \frac{1.64}{1.9} < 0 \)
Therefore, the solution to the inequality \( -1.9x^2 + 3.75 > 2.11 \) is:
\[ x^2 - \frac{1.64}{1.9} < 0 \]