/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 92 Solve each formula for the speci... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 92

Solve each formula for the specified variable. $$ P=2(a+b) \text { for } b $$

Short Answer

Expert verified
b = \frac{P}{2} - a.

Step by step solution

01

Isolate the term containing b

Start by isolating the term that contains the variable b. The original formula is \[P = 2(a + b)\] Divide both sides of the equation by 2:\[ \frac{P}{2} = a + b \]
02

Solve for b

Subtract a from both sides to solve for b:\[ \frac{P}{2} - a = b \]
03

Express the final answer

Rewrite the equation to explicitly show b:\[ b = \frac{P}{2} - a \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Isolating Variables
When solving equations, the first crucial step is often isolating the variable you are solving for. This means we need to get the variable alone on one side of the equation. In our example, the goal is to solve for the variable 'b' in the equation \[P = 2(a + b)\] To begin isolating 'b', we need to first move or eliminate any terms or coefficients that are affecting it. The approach is systematic:
  • Identify the term containing 'b'
  • Move all other terms to the opposite side of the equation
  • Keep the balance by performing same operations on both sides
By following these steps, you can make 'b' the subject of the formula easily.
Algebraic Manipulation
Algebraic manipulation involves rearranging the terms in an equation to solve for a variable. This includes adding, subtracting, multiplying, or dividing both sides of the equation as needed. In our example, after identifying the term with 'b' \[P = 2(a + b)\] the next step was to divide both sides by 2 to simplify the equation. This gave us: \[\frac{P}{2} = a + b\]
By doing this, we removed the coefficient of 2 affecting the term with 'b'. Algebraic manipulation allowed us to perform the same operation on both sides of the equation, maintaining the equation's balance.
Formula Rearrangement
Formula rearrangement is the process of rewriting a formula to express it in terms of a different variable. In this case, we need to rewrite the formula in terms of 'b'. After simplifying to \[ \frac{P}{2} = a + b \] the next step was to isolate 'b' itself. We did this by subtracting 'a' from both sides, resulting in \[ \frac{P}{2} - a = b \] Finally, we wrote the expression in a more standard form: \[ b = \frac{P}{2} - a \] Now, the formula is rearranged to show 'b' as the subject. Formula rearrangement lets us adapt equations to different contexts and solve for specific unknowns, making it a very useful skill in mathematics.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve each problem. (Assume that all items are equally priced.) (In Exercises 53鈥�56, round answers to the nearest tenth.) On a world globe, the distance between Rio de Janeiro and Hong Kong, two cities that are actually \(17,615 \mathrm{km}\) apart, is 21.5 in. The actual distance between Paris and Stockholm is \(1605 \mathrm{km} .\) How far apart are Paris and Stockholm on this globe?

Solve each problem. What is \(26 \%\) of \(480 ?\)

Translate each statement into an inequality. Use \(x\) as the variable. Tracy could spend at most \(\$ 20\) on a gift.

Find the value of \(y\) when \((a) x=-2\) and \((b) x=4 .\) Sections 1.3 and 2.3 $$ y+3 x=8 $$

Write an equation using the information given in the problem. Use \(x\) as the variable. Then solve the equation. If twice a number is divided by \(5,\) the result is \(4 .\) Find the number.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.