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Chapter 2: Problem 15

Solve each formula for the specified variable. \(P=2 L+2 W\) for \(L\)

Short Answer

Expert verified
L = \( \frac{P - 2W}{2} \)

Step by step solution

01

Identify the Variable to Solve For

The given equation is:\[P = 2L + 2W\]The task is to solve for the variable \(L\).
02

Isolate the Term Involving the Variable

Subtract \(2W\) from both sides of the equation to isolate the term involving \(L\):\[P - 2W = 2L\]
03

Solve for the Variable

Divide both sides of the equation by 2 to solve for \(L\):\[L = \frac{P - 2W}{2}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

headline of the respective core concept
Isolating variables is a crucial skill in solving equations, especially when dealing with linear equations. When we isolate a variable, we are essentially solving the equation for that particular variable, meaning we want to get this variable by itself on one side of the equation. For the exercise given, we are required to solve for the variable 'L'. The key steps to isolate 'L' involve moving other terms to the opposite side of the equation.
headline of the respective core concept
Algebraic manipulation involves performing operations on both sides of an equation to keep it balanced. In our example, we start with the equation:

\[P = 2L + 2W\]

To solve for L, we first perform an algebraic manipulation by subtracting 2W from both sides of the equation:

\[P - 2W = 2L\]

This step ensures that terms involving L are isolated to one side. Next, we further manipulate the equation by dividing both sides by 2, hence:

\[L = \frac{P - 2W}{2}\]

By systematically applying these operations, we isolate our desired variable.
headline of the respective core concept
Linear equations are equations where the highest power of the variable is 1. They often come in the form of ax + by = c. In the provided exercise:

\[P = 2L + 2W\]

we are dealing with a linear equation in two variables, L and W. The aim is to solve for L in terms of P and W. Using the steps of isolating variables and algebraic manipulation, we arrive at:

\[L = \frac{P - 2W}{2}\]

This final form shows that L is expressed linearly in terms of P and W. Understanding how to work with linear equations and perform the necessary algebraic operations is fundamental in mathematics.

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