1. The problem is to perform a manual solution, but since no specific problem was given, I will demonstrate solving a simple linear equation: $2x + 3 = 7$. 2. The formula or approach used here is to isolate the variable $x$ by performing inverse operations. 3. First, subtract 3 from both sides: $$2x + 3 - 3 = 7 - 3$$ which simplifies to $$2x = 4$$ 4. Next, divide both sides by 2 to solve for $x$: $$\frac{2x}{\cancel{2}} = \frac{4}{\cancel{2}}$$ which simplifies to $$x = 2$$ 5. Therefore, the solution to the equation $2x + 3 = 7$ is $x = 2$. This method can be applied to similar linear equations by performing inverse operations step-by-step to isolate the variable.