Let's start with the first one: $6b+3<15$. To isolate $b$, we subtract $3$ from both sides of the inequality:
\[6b+3-3<15-3\]
which simplifies to:
\[6b<12\]
Then, we divide both sides by $6$ to solve for $b$:
\[b<\frac{12}{6}\]
which simplifies to:
\[b<2\]
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