Final answer:
The biggest barriers to the success of the 15th Amendment were resistance from state officials, discrimination and violence against African Americans, and the imposition of arbitrary qualifications by states.
Step-by-step explanation:
One of the biggest barriers to the success of the 15th Amendment was the resistance from state officials to enforce it, despite the existing federal anti-discrimination laws. This resistance resulted in discrimination and violence against African Americans who tried to exercise their right to vote, including lynchings and vigilante executions. Additionally, states found ways to deny African Americans the right to vote through arbitrary qualifications such as literacy or property ownership.