1. The problem is to solve the equation $7x + 35 = 35$ for $x$. 2. We use the basic algebraic principle that to isolate $x$, we perform inverse operations on both sides of the equation. 3. Start by subtracting 35 from both sides: $$7x + 35 - 35 = 35 - 35$$ which simplifies to $$7x = 0$$ 4. Next, divide both sides by 7 to solve for $x$: $$x = \frac{0}{7} = 0$$ 5. Therefore, the solution to the equation is $x = 0$. This means when $x$ is zero, the expression $7x + 35$ equals 35, satisfying the equation.