To add \(-3\) and \(-17\), you can use the properties of addition:
\[ -3 + (-17) = -3 - 17 \]
When adding two negative numbers, you add their absolute values and keep the negative sign:
\[ 3 + 17 = 20 \] So,
\[ -3 + (-17) = -20 \]
Therefore, the answer is \(-20\).