/*! 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 39 Solve. $$ q=\frac{p+r}{2}, \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 15: Problem 39

Solve. $$ q=\frac{p+r}{2}, \text { for } p $$

Short Answer

Expert verified
The solution for \( p \) is \( p = 2q - r \).

Step by step solution

01

Understand the Given Equation

The given equation is \( q = \frac{p + r}{2} \). The goal is to solve this equation for the variable \( p \).
02

Clear the Fraction

To eliminate the fraction, multiply both sides of the equation by 2. This gives: \[ 2q = p + r \]
03

Isolate the Variable \( p \)

Subtract \( r \) from both sides of the equation to isolate \( p \). This gives: \[ p = 2q - r \]

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.

Linear Equations
Linear equations form the cornerstone of algebra. They typically look like this: y = mx + bwhere y and x are variables, and m and b are constants. Linear equations can have various forms, such as the standard form Ax + By = C. Understanding linear equations is crucial because they model simple relationships between two quantities. In many problems, particularly those involving basic algebra, you will often need to manipulate these equations to solve for a particular variable.
Fraction Elimination
One common challenge in solving equations is dealing with fractions. Fractions can make equations look complicated, but we can often simplify them by eliminating the fractions entirely. For example, suppose you have an equation like this: y = \( \frac{x+5}{3} \)To get rid of the fraction, you can multiply both sides of the equation by 3: 3y = x+5This process, known as fraction elimination, makes the equation easier to solve. Once the fraction is eliminated, you can proceed with isolating the variable.
Algebraic Manipulation
After eliminating fractions, algebraic manipulation is the next step. This involves rearranging the equation to isolate the variable you're trying to solve for. Let's see this in action with a simplified version of our starting equation: y = 2x + 3 To solve for x, you would first subtract 3 from both sides: y - 3 = 2x Next, divide both sides by 2: \( \frac{y-3}{2} = x\) Thus, x has been isolated. Similar steps are followed in more complex equations, making algebraic manipulation techniques essential for any algebra student.

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

Determine whether the given number is a solution of the given equation. $$ -3 ; 4-x=1 $$

Solve each system using the substitution method. $$ \begin{aligned} &m-2 n=16\\\ &n=1-4 m \end{aligned} $$

Solve each system using the elimination method. $$ \begin{array}{r} {2 x+y=6} \\ {x-y=3} \end{array} $$

Combine like terms. $$ 4 m+10-5 m+12 $$

Multiply. $$ -2(15-3 x) $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Decision Maths

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.