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In mathematics, isolating variables is a central technique when solving equations. It means rearranging the equation so the variable of interest stands alone on one side of the equation.
This often involves using inverse operations like addition, subtraction, multiplication, or division to move other terms to the opposite side.
Every time we perform an operation on one side of an equation, we must also perform it on the other side to maintain equality.
For example, in step 2 of our solution: Subtracting \(2L\) from both sides simplifies \(P = 2L + 2W\) to \(P - 2L = 2W\).
This technique is foundational to solving linear equations and many other types of equations.

The perimeter formula for a rectangle helps determine the total length around the shape.
This is essential in geometry for finding distances and is usually expressed in terms of the lengths of the sides.
For a rectangle, the perimeter formula is given by: \(P = 2L + 2W\).

• \(P\): Perimeter
• \(L\): Length
• \(W\): Width

If you know three of the four quantities, you can always solve for the fourth by rearranging the formula and isolating the unknown variable.
In our given exercise, we are solving for width \(W\). By isolating \(W\) in the formula \(P = 2L + 2W\), we find how wide a rectangle must be to have a specified length and perimeter.

Linear equations involve variables that are raised only to the first power and graphically represent straight lines. These are the simplest form of algebraic equations.
In general, a linear equation looks like \(ax + b = c\).
When solving linear equations, the process typically begins with isolating the variable by performing operations that simplify the equation.
In the provided exercise, the equation \(P = 2L + 2W\) is a linear equation that relates perimeter, length, and width of a rectangle.
Once you subtract \(2L\) from both sides, you obtain another linear equation: \(P - 2L = 2W\).
Finally, divide every term by 2 to isolate \(W\): \[(P - 2L)/2 = W\].
Linear equations are straightforward and form the basis for understanding more complex algebraic concepts.