1. **Problem:** Add the linear expressions (12x + 5) + (-10x - 3). 2. **Formula:** To add linear expressions, combine like terms (terms with the same variable) by adding their coefficients. 3. **Work:** $$(12x + 5) + (-10x - 3) = 12x + 5 - 10x - 3$$ Combine like terms: $$12x - 10x + 5 - 3$$ $$= (12 - 10)x + (5 - 3)$$ $$= 2x + 2$$ 4. **Explanation:** We added the coefficients of $x$ (12 and -10) to get 2, and the constants 5 and -3 to get 2. 5. **Final answer:** $$2x + 2$$