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When solving equations, the main goal is to find the value of the variable that makes the equation true. This involves a series of logical steps and operations that simplify the equation. For example, operations such as addition, subtraction, multiplication, and division are commonly used to manipulate the terms in the equation. Each operation should be carefully done on both sides of the equation to maintain balance and equality. The final aim is to isolate the variable on one side of the equation as much as possible. This often involves reversing operations to break down the equation into simpler parts. Solving equations might involve more complex steps like factoring or using formulas in certain cases. Regardless of their complexity, all equations require a strategic approach to reach the solution. Work systematically and check your solution by substituting it back into the original equation to ensure its validity.

Square root equations are a specific type of equation where the variable is inside a square root. These can initially look complex due to the square root, but they follow a predictable method to solve. The first step is usually isolating the square root on one side of the equation so that it stands alone. This might involve doing addition or subtraction as seen in the given exercise. Once isolated, the next step is to eliminate the square root by squaring both sides of the equation. This step is crucial as it simplifies the equation to a linear form, making it much easier to solve. However, one must be careful. Squaring both sides can introduce extraneous solutions—solutions that do not satisfy the original equation. Thus, always substitute your solution back to check if it holds true in the initial equation.

After eliminating the square root from a square root equation by squaring, the resulting equation is often linear. Linear equations are the simplest form of equations where the highest power of the variable is one. Solving linear equations typically involves straightforward algebraic manipulation. In our example, after squaring both sides we were left with a simple equation, \(3x = 16\). The goal is to isolate the variable \(x\). This usually involves reversing multiplication or division. Divide both sides by the coefficient of \(x\) to find the value of \(x\). For \(3x = 16\), dividing both sides by 3 yields \(x = \frac{16}{3}\). This final answer is the solution to the linear equation derived from the original problem. Linear equations are foundational in algebra and understanding them well can assist in solving more complex equations effectively.