Question

We, the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution of the United States of America.
How did the 15th, 19th, and 26th Amendments expand the "Blessings of Liberty" to more of the United States' population?

Answer 1

15th: The 15th amendment outlawed the ability for a state to deny a citizen's right to vote based on race, color, or past servitude. This allowed more people the right to the liberties others had, promoting general welfare among all races.

19th: The 19th amendment made it so that a state could not deny the right for a citizen to vote based on gender. Similar to the 15th amendment, the Blessings of Liberty had been bestowed among more people, as now all genders had the right to vote.

26th: The 26th amendment stated that everyone over the age of 18 has the right to vote, and no age discrimination is to take place. This granted more liberty to those who were once unable to vote. This was the final of the amendments, meaning that now all races, genders, and everyone 18+ is given the freedom to partake in our elections.

I hope I've helped! :)