Subjects algebra

Expression Simplification C7B05E

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1. **State the problem:** Simplify the expression $2\{3(a+2b)+(c+d-4)\}+5$. 2. **Apply the distributive property inside the braces:** $$3(a+2b) = 3a + 6b$$ 3. **Rewrite the expression inside the braces:** $$3a + 6b + c + d - 4$$ 4. **Multiply the entire expression inside the braces by 2:** $$2 \times (3a + 6b + c + d - 4) = 2 \times 3a + 2 \times 6b + 2 \times c + 2 \times d - 2 \times 4$$ $$= 6a + 12b + 2c + 2d - 8$$ 5. **Add the remaining +5 outside the braces:** $$6a + 12b + 2c + 2d - 8 + 5$$ 6. **Combine like terms:** $$-8 + 5 = -3$$ 7. **Final simplified expression:** $$6a + 12b + 2c + 2d - 3$$ This is the simplified form of the given expression.