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The core of the Triple Alliance was Germany and Austria-Hungary who promised to protect each other against attack by any third party. Italy was an "adjunct" member, who promised and was promised protection against attack only by France. But Italy "opted out" because Austria-Hungary had violated a clause in the treaty to consult with Italy before changing the status quo in the Balkans (Austria-Hungary did not do so before attacking Serbia.)
The Achilles heel of the alliance was that Italy and Austria-Hungary basically hated each other, perhaps even more than either hated France. Each feared "retaliation" by the other; Italy in Venice, Austria-Hungary in Tyrol.
Italy "got around" to joining the Allies in 1915 when they promised her Tyrol and Trieste as spoils of war. (Ironically, Germany and Austria-Hungary even offered her South Tyrol to rejoin them.)