/*! 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 44 Solve each formula for the indic... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 44

Solve each formula for the indicated letter. $$ S=r x+s x, \text { for } x $$

Short Answer

Expert verified
x = .

Step by step solution

01

Identify the given equation

The given equation is \(S = rx + sx\). The goal is to solve this equation for \(x\).
02

Factor \(x\) out

Notice that \(x\) is a common term on the right-hand side of the equation. Factor \(x\) to simplify: \(S = x(r + s)\).
03

Solve for \(x\)

To isolate \(x\), divide both sides of the equation by \(r + s\): \(x = \frac{S}{r + s}\).

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.

Factoring
Factoring is an essential technique in algebra. It involves breaking down an expression into simpler parts that, when multiplied together, give the original expression.
In the given problem, we have the equation: \(S = rx + sx\). Notice that both terms on the right side of the equation share a common factor, \(x\).
To factor \(x\) out, we rewrite the equation as: \(S = x(r + s)\). This step simplifies the process of solving for the variable.
Factoring helps transform complex expressions into simpler forms, making it easier to work through algebraic problems.
Isolating Variables
Isolating variables is a key step in solving equations. It means getting the variable you're solving for by itself on one side of the equation.
In our starting equation: \(S = rx + sx\), our goal is to solve for \(x\). After factoring, the equation becomes \(S = x(r + s)\).
Here, \(x\) is already grouped together, but it needs to be completely by itself. To isolate \(x\), we divide both sides by \(r + s\), resulting in \(x = \frac{S}{r + s}\).
This step-by-step process of isolating the variable helps in arriving at the solution methodically.
Algebraic Manipulation
Algebraic manipulation involves using various algebraic operations like addition, subtraction, multiplication, division, and factoring to rearrange and simplify equations.
In the given equation, \(S = rx + sx\), we used factoring to make the equation simpler, resulting in \(S = x(r + s)\).
Next, we used division, an algebraic operation, to isolate \(x\). By dividing both sides by \(r + s\), we obtain the solution \(x = \frac{S}{r + s}\).
Understanding and applying these algebraic techniques can make solving equations more straightforward and less intimidating.

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

Use an inequality and the five-step process to solve each problem. Reduced Fat Oreo " cookies contain 4.5 of fat per serving. In order for a food to be labeled "reduced fat," it must have at least \(25 \%\) less fat than the regular item. What can you conclude about the number of grams of fat in a serving of the regular Oreo cookies?

Solve for \(x\) $$ \frac{1}{2}(2 x+2 b)>\frac{1}{3}(21+3 b) $$

Review operations with real numbers. Simplify. $$ \frac{1-(-7)}{-3-5} $$

Use an inequality and the five-step process to solve each problem. As part of an outdoor education course, Tricia needs to make a bright-colored triangular flag with an area of at least \(3 \mathrm{ft}^{2} .\) What heights can the triangle be if the base is \(1 \frac{1}{2} \mathrm{ft} ?\) (THE IMAGE CANNOT BE COPY)

To prepare for Section 2.5, review translating to algebraic expressions and equations. Translate to an algebraic expression or equation. Erin is returning a tent that she bought during a \(25 \%\) off storewide sale that has ended. She is offered store credit for \(125 \%\) of what she paid (not to be used on sale items). Is this fair to Erin? Why or why not?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Logic and Functions

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.