Set 11: Linear Equations

Choice D is correct. Choice D is the correct answer. To isolate the variable, we divide by the coefficient. 1. Start with the equation: $9x = 81$ 2. Divide both sides by 9: $x = \frac{81}{9}$ 3. Simplify: $x = 9$ 4. Verify: $9(9) = 81$ ✓ This is a perfect square relationship: $9^2 = 81$, so when we divide 81 by 9, we get 9 back. Pattern Recognition: Recognizing that $81= 9 \times 9$ helps you solve this mentally. Choice B is incorrect because this results from subtracting: $81- 9 = 72$. Subtraction is not the inverse of multiplication. Choice C is incorrect because this comes from adding: $81+ 9 = 90$. Addition doesn't undo multiplication. Choice A is incorrect because this results from multiplying: $81\times 9 = 729$. This compounds the multiplication instead of reversing it.