Set 11: Linear Equations

Choice D is correct. Choice Ahoice C is the correct answer. When a number is being subtracted from the variable, we add to both sides to solve. 1. Start with the equation: $x - 7 = 15$ 2. Identify the operation: 7 is being subtracted from $x$ 3. Apply the inverse operation: Add 7 to both sides 4. Simplify: $x = 15 + 7 = 22$ 5. Verify: $22- 7 = 15$ ✓ Remember: The inverse of subtraction is addition. To undo "minus 7", we add 7. Choice A is incorrect because this results from subtracting 7 from 15 instead of adding: $15- 7 = 8$. This applies the same operation instead of the inverse. Choice C is incorrect because this is the negative of Choice A. Some students might calculate $15- 7$ and then incorrectly apply a negative sign, getting $-8$. Choice D is incorrect because this confuses the constant being subtracted (7) with the solution. The number 7 appears in the equation, but it's not the value of $x$.