"support your decision" is a correct and usable phrase in written English.
You can use it when discussing a decision that has been made or is going to be made. For example: "I will support your decision, no matter what it may be."
Support your decision with concrete evidence.
"I cannot in good conscience support your decision to pardon former President Nixon even before he has been charged with the commission of any crime," Mr. terHorst wrote to Ford in his resignation letter on Sept. 8, 1974.
"But if you think publicizing this will create a scandal that harms your reputation and might lead to acts that could be avoided" -- a reference to revenge by her relatives -- "then I support your decision not to file a complaint and I ask you to pay attention to your health").
Russell adds: "Negotiate your options, look for win-win solutions, and if you have to say 'no' to a statutory request to work flexibly, give one of the permissible reasons, for example, not enough work being available at the times requested, and have concrete evidence to support your decision.
Big Data and its compilation should be able to provide you, the business leader, with "fast" facts to support your decision making.
Ask your board member on the spot if they support your decision and whether she sees any weaknesses in your approach.
I'm sorry that your family will say they support your decisions and that they love you, but won't honor your new last name.
I will support your decisions with the children, have them to your house on time, and never talk badly about you to the children.
The child will be more likely to support your decisions, and that will help the family stay in harmony through the financial crisis.
I can guarantee you'll be able to find evidence — probably enough to write a thesis — that supports your decision.
Be happy that your parents are supporting your decision, if they did.
