According to question,
\[\left( 4x\text{ }+\text{ }5 \right)/2\text{ }>\text{ }\left( 5x\text{ }+\text{ }6 \right)/3\]
[Taking L.C.M]
\[3\text{ }\left( 4x\text{ }+\text{ }5 \right)\text{ }>\text{ }2\text{ }\left( 5x\text{ }+\text{ }6 \right)\]
[On cross-multiplication]
\[12x\text{ }+\text{ }15\text{ }>\text{ }10x\text{ }+\text{ }12\]
\[12x\text{ }\text{ }10x\text{ }>\text{ }12\text{ }\text{ }15\]
\[2x\text{ }>\text{ }-3\]
\[x\text{ }>\text{ }-3/2\]
Hence,
for x ∈ I the smallest value of x is -1.