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When solving equations, the first major step is commonly known as the isolation of variables. This is essential because it allows us to find the value of the unknown variable that makes the equation true. The goal is to get the variable, often represented as \( x \), completely alone on one side of the equation. To isolate \( x \) in the equation \(2 = x - 11\), you need to eliminate any numbers that are directly affecting \( x \).

In our example, \( -11 \) is subtracted from \( x \). We perform the opposite operation to both sides of the equation to maintain balance. This means adding \( 11 \) to both sides, effectively canceling out the \( -11 \):

• Start with: \( 2 = x - 11 \)
• Add: \( 2 + 11 = x - 11 + 11 \)
• Result: \( 13 = x \)

Once the numbers on one side are eliminated, the variable \( x \) stands alone, and isolation is achieved. This isolation is key in pinpointing exactly what \( x \) is equal to.

After isolating the variable, the next step is to simplify the equation. Simplifying an equation means reducing it to its most basic form, where the solution is clearly visible. In our situation, once we add \( 11 \) to both sides, we end up with \( 13 = x \). This is already in a simplified form, indicating that the work is practically finished.

Simplification often involves basic arithmetic operations such as addition, subtraction, multiplication, or division. However, in this example, those operations were minimal as the equation easily led to the solution.

• Equation after isolating: \( 13 = x \)
• No further simplification needed

The simplified form provides a clear and straightforward answer to the question, revealing that \( x \) equals \( 13 \).

A linear equation is an equation in which the highest power of the variable is one. This type of equation is typically represented in the form \( ax + b = c \), where \( a \), \( b \), and \( c \) are constants. In our example, \( 2 = x - 11 \) fits this model, meaning it is a simple linear equation.

The characteristic of linear equations is that they graph as straight lines when plotted on a coordinate plane. Each solution corresponds to a point on this line. Solving a linear equation, like in our task, involves finding which specific point makes the equation true. In our case, it indicates that when \( x \) is \( 13 \), the line crosses the point where both sides of the equation are equal.

• Equation of the linear form: \( x - 11 = 2 \)
• Solve to find when values balance: \( x = 13 \)

Understanding linear equations is crucial because they are foundational for algebraic study and solve many real-world problems.