To solve the inequality \( 14 + 10y \geq 3(y + 14) \), we can start by distributing the \( 3 \) on the right side of the inequality:
\[ 14 + 10y \geq 3y + 42 \]
Next, we will rearrange the inequality to get all terms involving \( y \) on one side and the constant terms on the other side. We can subtract \( 3y \) from both sides:
\[ 14 + 10y - 3y \geq 42 \]
This simplifies to:
\[ 14 + 7y \geq 42 \]
Now, we subtract \( 14 \) from both sides:
\[ 7y \geq 42 - 14 \] \[ 7y \geq 28 \]
Next, we divide both sides by \( 7 \):
\[ y \geq 4 \]
Thus, the solution to the inequality is:
\[ \boxed{y \geq 4} \]