Mathematics

The key insight is that an equation is a balance—both sides have equal value. When you subtract the same number from both sides, you preserve that equality, like removing the same weight from both pans of a balanced scale. The solution $x$ represents the specific value that makes the equation true, and since you're treating both sides identically, whatever value satisfied the original equation will satisfy the new one too.

The key insight is that an equation is a balance—both sides have equal value. When you subtract the same number from both sides, you preserve that equality, like removing the same weight from both pans of a balanced scale. The solution $x$ represents the specific value that makes the equation true, and since you're treating both sides identically, whatever value satisfied the original equation will satisfy the new one too.