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Understanding the process of isolating the variable is crucial when it comes to solving linear equations. Isolating the variable means rearranging the equation so that the variable we are solving for is by itself on one side of the equality sign, and everything else is on the other side. For the equation
\(4 = x - 11\),
the main objective is to get 'x' on one side and all the numerical values on the other. To achieve this, one can perform operations such as addition, subtraction, multiplication, or division to both sides of the equation, keeping the balance of the equation intact.
For instance, in our exercise, by adding 11 to both sides
\(4 + 11 = x - 11 + 11\),
you counteract the subtraction of 11 on the right side, effectively simplifying the equation to
\(15 = x\).
This step has successfully isolated 'x' and allowed you to progress towards finding the solution.

The process of solving an equation involves a series of clear and logical steps. Beginning with identifying the equation and determining what you are solving for is the first crucial step. Afterward, you look at what operations may be performed to isolate your variable. As seen in our example,
\(4 = x - 11\),
the steps involved adding 11 to both sides to cancel out the minus 11, thereby isolating 'x'.

Key Steps for Solving Equations

• Identify the Equation: Ensure you understand the structure and terms of the equation.
• Isolate the Variable: Use operations that help move terms to one side to focus on the variable.
• Simplify: Combine like terms and simplify both sides as much as possible.
• Solve: Perform the necessary operations to find the value of the variable.

These steps help maintain a methodical approach to solving equations and provide a path to follow that leads to a solution.

Once you believe you've found the solution to an equation, it's vital to verify its accuracy by checking the solution. You can do this by substituting the value of the variable back into the original equation to see if both sides equal.
In our example, with the equation
\(4 = x - 11\),
and the obtained solution
\(15 = x\),
you substitute 15 for 'x' back into the original equation to get
\(4 = 15 - 11\),
which simplifies to
\(4 = 4\).
This equality confirms the solution is correct. If both sides do not equal, it indicates a mistake was made somewhere in the solving process, and you need to retrace your steps to find and correct the error. Checking your solution not only ensures accuracy but also deepens the understanding of equation solving as a process.