1. **State the problem:** Solve the equation $2370 - 19x = 2700 - (1350 - 15x)$. 2. **Apply the distributive property:** Remove the parentheses on the right side by distributing the minus sign: $$2370 - 19x = 2700 - 1350 + 15x$$ 3. **Simplify the right side:** Calculate $2700 - 1350$: $$2370 - 19x = 1350 + 15x$$ 4. **Isolate variable terms on one side:** Add $19x$ to both sides to move all $x$ terms to the right: $$2370 - \cancel{19x} + 19x = 1350 + 15x + 19x$$ $$2370 = 1350 + 34x$$ 5. **Isolate constants on the other side:** Subtract $1350$ from both sides: $$2370 - 1350 = 1350 - \cancel{1350} + 34x$$ $$1020 = 34x$$ 6. **Solve for $x$:** Divide both sides by $34$: $$\frac{1020}{\cancel{34}} = \frac{34x}{\cancel{34}}$$ $$30 = x$$ **Final answer:** $x = 30$