Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

1. Equations & Inequalities

Linear Equations

College Algebra

1. Equations & Inequalities

Linear Equations

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1:48 minutes

Problem 42

Textbook Question

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

Start with the formula for the perimeter of a rectangle: \( P = 2l + 2w \).

To solve for \( w \), first isolate the terms involving \( w \) by subtracting \( 2l \) from both sides: \( P - 2l = 2w \).

Now, to solve for \( w \), divide both sides of the equation by 2: \( w = \frac{P - 2l}{2} \).

This gives you the expression for \( w \) in terms of \( P \) and \( l \).

Remember, this solution assumes that the perimeter \( P \) and length \( l \) are known, and the denominator is not zero.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Perimeter of a Rectangle

The perimeter of a rectangle is the total distance around the rectangle, calculated by the formula P = 2l + 2w, where l is the length and w is the width. Understanding this formula is essential for solving for either variable when given the perimeter.

Algebraic Manipulation

Algebraic manipulation involves rearranging equations to isolate a specific variable. This includes operations such as adding, subtracting, multiplying, or dividing both sides of the equation to solve for the desired variable, in this case, w.

Assumption of Non-Zero Denominator

In algebra, it is crucial to assume that any variable in the denominator of a fraction is not equal to zero, as division by zero is undefined. This assumption ensures that the solutions derived from the equations are valid and applicable.