1. The problem is to understand why we add one to both sides of an equation. 2. When solving equations, the goal is to isolate the variable on one side. 3. To keep the equation balanced, whatever operation you do to one side, you must do to the other side. 4. Adding one to both sides is an example of this rule: if you add 1 to the left side, you must add 1 to the right side to maintain equality. 5. For example, if you have $x - 1 = 3$, adding 1 to both sides gives: $$x - 1 + 1 = 3 + 1$$ 6. Simplifying, we get: $$x = 4$$ 7. This step helps to cancel out the $-1$ on the left side, isolating $x$. 8. In summary, adding the same number to both sides keeps the equation balanced and helps solve for the variable.