1. **Problem:** Andre claims that the expressions $10x + 6$ and $5x + 11$ are equivalent because both equal 16 when $x=1$. 2. **Formula and rule:** Two expressions are equivalent if they are equal for all values of $x$, not just one. 3. **Evaluate both expressions at $x=1$: ** $$10(1) + 6 = 10 + 6 = 16$$ $$5(1) + 11 = 5 + 11 = 16$$ They are equal at $x=1$. 4. **Check equivalence for another value, say $x=0$: ** $$10(0) + 6 = 6$$ $$5(0) + 11 = 11$$ They are not equal at $x=0$. 5. **Conclusion:** Since the expressions are not equal for all $x$, they are not equivalent. Andre is incorrect. --- 2. **Problem:** Find all expressions that can be subtracted from $9x$ to get $3x + 5$. 3. **Formula:** If $9x - E = 3x + 5$, then $E = 9x - (3x + 5) = 6x - 5$. 4. **Check each option:** - A: $-5 + 6x = 6x - 5$ (same as $6x - 5$) ✔ - B: $5 - 6x$ (not equal to $6x - 5$) ✘ - C: $6x + 5$ (not equal to $6x - 5$) ✘ - D: $6x - 5$ (exact match) ✔ - E: $-6x + 5$ (not equal) ✘ 5. **Answer:** A and D. --- 3. **Problem:** Identify which statements are true for any value of $x$. 4. **Check each statement:** A. $7x + (2x + 7) = 7x + 2x + 7 = 9x + 7$ ✔ B. $7x + (2x - 1) = 9x - 1 eq 9x + 1$ ✘ C. $\frac{1}{2}x + (3 - \frac{1}{2}x) = \frac{1}{2}x + 3 - \frac{1}{2}x = 3$ ✔ D. $5x - (8 - 6x) = 5x - 8 + 6x = 11x - 8 eq -x - 8$ ✘ E. $0.4x - (0.2x + 8) = 0.4x - 0.2x - 8 = 0.2x - 8$ ✔ F. $6x - (2x - 4) = 6x - 2x + 4 = 4x + 4$ ✔ 5. **True statements:** A, C, E, F.