1. **Problem Statement:** Simplify the expression by combining like terms and using the distributive property. 2. **Key Concepts:** - Combining like terms means adding or subtracting terms with the same variable and exponent. - The distributive property states that $a(b + c) = ab + ac$. - Parentheses affect the signs of terms inside when preceded by a minus sign. 3. **Example:** Simplify $3x + 2(4x - 5) - (x - 3)$. 4. **Step 1: Apply the distributive property:** $$3x + 2 \times 4x - 2 \times 5 - 1 \times x + 1 \times 3$$ $$= 3x + 8x - 10 - x + 3$$ 5. **Step 2: Combine like terms:** $$3x + 8x - x = (3 + 8 - 1)x = 10x$$ $$-10 + 3 = -7$$ 6. **Final simplified expression:** $$10x - 7$$ This shows how to distribute multiplication over addition/subtraction and combine like terms carefully, especially handling signs inside parentheses.