Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. P=2l+2w,for w (perimeter of a rectangle)

Verified step by step guidance

1. Start with the given formula for the perimeter of a rectangle: \(P = 2l + 2w\).
2. Our goal is to solve for \(w\), so first isolate the terms involving \(w\) by subtracting \$2l\( from both sides: \)P - 2l = 2w$.
3. Now, to solve for \(w\), divide both sides of the equation by 2: \(\frac{P - 2l}{2} = w\).
4. Rewrite the equation to clearly express \(w\) in terms of \(P\) and \(l\): \(w = \frac{P - 2l}{2}\).
5. This is the formula for \(w\) in terms of \(P\) and \(l\), assuming the denominator (2) is not zero.

Key Concepts

Solving Linear Equations

Solving linear equations involves isolating the variable of interest on one side of the equation using inverse operations such as addition, subtraction, multiplication, and division. The goal is to rewrite the equation so that the specified variable is expressed explicitly in terms of the other variables or constants.

Understanding Formulas and Variables

A formula expresses a relationship between variables. To solve for a specific variable means to rearrange the formula so that variable stands alone on one side. This requires recognizing which terms contain the variable and manipulating the equation accordingly.

Avoiding Division by Zero

When solving equations, especially those involving variables in denominators, it is important to ensure the denominator is not zero, as division by zero is undefined. This assumption allows safe manipulation of the equation without invalid solutions.