1. **State the problem:** Calculate the value of the expression $$17 + 3 | -5 + (-2) |$$. 2. **Understand the absolute value:** The absolute value of a number is its distance from zero on the number line, always non-negative. For any number $x$, $|x| = x$ if $x \geq 0$, and $|x| = -x$ if $x < 0$. 3. **Calculate inside the absolute value:** $$-5 + (-2) = -5 - 2 = -7$$ 4. **Apply the absolute value:** $$| -7 | = 7$$ 5. **Substitute back into the expression:** $$17 + 3 \times 7$$ 6. **Multiply:** $$3 \times 7 = 21$$ 7. **Add:** $$17 + 21 = 38$$ **Final answer:** $$38$$