5-1. Solve the inequality

$$
\sqrt{3 x-7}-\sqrt{3 x^{2}-13 x+13} \geqslant 3 x^{2}-16 x+20
$$

In your answer, specify the sum of all integer values of $x$ that satisfy the inequality.
Solution. As a result of the substitution $v=\sqrt{3 x-7}, u=\sqrt{3 x^{2}-13 x+13}$, we obtain the equivalent inequality $u \leqslant v$. Therefore, $x$ satisfies the inequality $3 x^{2}-13 x+13 \leqslant 3 x-7 \Longleftrightarrow 2 \leqslant x \leqslant 10 / 3$. Out of the two integer values $x=2$ and $x=3$, only $x=3$ falls within the domain of valid values.

Answer: (B) 3.

Answer options.

![](https://cdn.mathpix.com/cropped/2024_05_06_997c53c06135e2de9c16g-05.jpg?height=70&width=638&top_left_y=525&top_left_x=760)