1. **State the problem:** Solve the inequality $$-38d - 57 \geq -19d + 76$$ for $d$. 2. **Isolate the variable terms:** Add $38d$ to both sides to move all $d$ terms to the right side: $$-57 \geq -19d + 76 + 38d$$ Simplify the right side: $$-57 \geq 19d + 76$$ 3. **Isolate the constant terms:** Subtract $76$ from both sides: $$-57 - 76 \geq 19d$$ Simplify: $$-133 \geq 19d$$ 4. **Solve for $d$:** Divide both sides by $19$. Since $19$ is positive, the inequality direction stays the same: $$\frac{-133}{19} \geq d$$ 5. **Rewrite the solution:** $$d \leq \frac{-133}{19}$$ 6. **Reduce the fraction:** $133$ and $19$ have no common factors other than $1$, so the fraction is already in lowest terms. **Final answer:** $$d \leq -\frac{133}{19}$$