You can still activate the -6 ability however. The cost isn't :[+1} + {-6]". The way the rule is written is that, instead, the cost simply becomes [-5]. And Solemnity doesn't prevent you from removing counters which is all [-5] is trying to do.
Yes. The activation cost would be [-5], and Solemnity will not interfere with that payment.
Modern Horizons 2 Release Notes
* The total cost of a planeswalker’s loyalty ability is calculated before any counters are added or removed. If a loyalty ability normally costs [-3] to activate, you do not remove three counters from it and then put one counter on it. You remove two counters at one time when you pay the cost.
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Why bother with mere rulings when so many answers can be found in the Rules?
I think Gideon Blackblade enters the battlefield as a creature AND a planeswalker if you cast it on your turn. So, if it's your turn and you cast Gideon Blackblade, I think Rezzachan would be correct that no counters can be placed on Gideon Blackblade. So, it would die on your opponent's turn, since it has no loyalty counters and is not a creature.
If you were to cast Gideon Blackblade on an opponent's turn, you would get the loyalty counters, because it's not a creature. Once your turn starts, you can remove loyalty counters, but you cannot add them as Gideon is a creature on your turn.
If Solemnity is already on the field and Gideon is entering, this would cause Gideon to enter with 0 counters, as mentioned, as well as just die right away. It doesn't wait for the opponent's turn; he will die immediately.
Can I activate Gideon's +1?
Can I activate Gideon's -6?
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Yes. The activation cost would be [-5], and Solemnity will not interfere with that payment.
I think Gideon Blackblade enters the battlefield as a creature AND a planeswalker if you cast it on your turn. So, if it's your turn and you cast Gideon Blackblade, I think Rezzachan would be correct that no counters can be placed on Gideon Blackblade. So, it would die on your opponent's turn, since it has no loyalty counters and is not a creature.
If you were to cast Gideon Blackblade on an opponent's turn, you would get the loyalty counters, because it's not a creature. Once your turn starts, you can remove loyalty counters, but you cannot add them as Gideon is a creature on your turn.
Otherwise, the rest of your comment is correct.