To solve the compound inequality $6x - 3 < 9$ and $2x + 9 \geq 3$, begin by solving each inequality. For the first, adding $3$ gives $6x < 12$, which simplifies to $x < 2$. For the second, subtracting $9$ gives $2x \geq -6$, which simplifies to $x \geq -3$. Graphing $x < 2$ results in shading to the left of an open parenthesis at $2$, while graphing $x \geq -3$ results in shading to the right of a bracket at $-3$. The final solution is the overlapping region, which spans from $-3$ up to $2$. In interval notation, this is written as $[-3, 2)$.