Subjects algebra

Expression Simplification A97E3D

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1. **State the problem:** Simplify the expression given by the top-left, top-right, and bottom-right parts: Top-left: $7 - \frac{24 - 4n}{2}$ Top-right: $\frac{4(3n + 1)}{2} - (2n + 3)$ Bottom-right: $3n - 7 - (-n - 6)$ 2. **Simplify top-left:** $$7 - \frac{24 - 4n}{2} = 7 - \frac{24}{2} + \frac{4n}{2}$$ $$= 7 - 12 + 2n$$ $$= (7 - 12) + 2n = -5 + 2n$$ 3. **Simplify top-right:** $$\frac{4(3n + 1)}{2} - (2n + 3) = \frac{12n + 4}{2} - 2n - 3$$ $$= 6n + 2 - 2n - 3$$ $$= (6n - 2n) + (2 - 3) = 4n - 1$$ 4. **Simplify bottom-right:** $$3n - 7 - (-n - 6) = 3n - 7 + n + 6$$ $$= (3n + n) + (-7 + 6) = 4n - 1$$ **Final simplified expressions:** - Top-left: $-5 + 2n$ - Top-right: $4n - 1$ - Bottom-right: $4n - 1$