6. (20 points). Solve the equation: $\sqrt{4+2 x}+\sqrt{6+3 x}+\sqrt{8+4 x}=9+\frac{3 x}{2}$
Solution: Notice that $4+2x=2(2+x); 6+3x=3(2+x); 8+4x=4(2+x)$, by the inequality of means, the left side does not exceed $(2+2+x+3+2+x+4+2+x) / 2=15 / 2+3x / 2$

Answer: no solutions.

## Criteria:

| Points | Conditions for awarding |
| :---: | :--- |
| 20 points | Any complete and correct solution |
| 15 points | The inequality of means is used, but an arithmetic error is made |
| 5 points | Only the answer is given |
| 0 points | The solution does not meet any of the criteria listed above. |

## Solution variant № 7