/*! 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 15 Solve for the indicated variable... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 15

Solve for the indicated variable. \(E=I R\) for \(I\)

Short Answer

Expert verified
The solution to the equation for \(I\) is \(I = E/R\).

Step by step solution

01

Identify Given Equation

The given equation is \(E = I R\). We are asked to solve this equation for \(I\). This implies that we need to isolate \(I\) on one side of the equation.
02

Isolate the Variable I

To solve for \(I\), we need to get \(I\) on one side of the equation. We can do this by dividing both sides of the equation by \(R\). Doing so gives us a new equation: \(I = E/R\).

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.

Solving Equations
When tasked with solving an algebraic equation, the ultimate goal is to find the value of the unknown variable. For instance, in our example, we need to find the value of \(I\).
To do this successfully, it often involves some basic algebraic steps such as addition, subtraction, multiplication, and division.
  • First, understand the equation. Check what is already known and what you need to find.
  • Next, decide on the best operation to isolate the desired variable.
  • Remember, every step you take should be legal in terms of algebraic operations.
In the given example \(E= I R\), the focus is on manipulating the equation to make \(I\) the subject. This approach is a classic example of how maintaining a logical sequence of steps can smoothly lead you to the solution.
Isolating Variables
Isolating a variable is a pivotal step in solving equations. It means you need to adjust the equation so that the variable you're solving for is alone on one side of the equation.
For our exercise \(E = I R\), we isolate \(I\) by getting rid of the accompanying term \(R\).
  • You achieve this by performing the inverse operation. Here, as \(I\) is multiplied by \(R\), we divide both sides by \(R\).
  • This division removes \(R\) from the right side, thus successfully isolating \(I\).
Such steps make equations simpler and easier to solve, allowing you to express the variable in terms of the other given values. It is a fundamental technique in algebra that comes in handy across various mathematical problems.
Formula Manipulation
Formula manipulation involves transforming equations to express a specific variable differently. This skill is vital in algebra where it's common to come across equations that need rearrangement.
In the scenario of \(E = I R\), formula manipulation helps rewrite it in terms of \(I\), resulting in \(I = \frac{E}{R}\).
  • This process can include moving terms across the equals sign or rewriting expressions.
  • It's all about understanding the relationship between different parts of the formula and ensuring the operations are correctly applied.
  • Formula manipulation often involves performing inverse operations carefully, making sure the equation preserves equality.
Mastering this skill enhances your ability to work flexibly with equations, adapting them to meet specific problem-solving needs. It's an essential tool in both academic settings and real-world applications.

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

A student invested \(90 \%\) of her savings in the stock market. If she invested \(\$ 4,050\) what are her total savings?

Given that \(K=\frac{1}{2} h(a+b),\) find \(h\) if \(K=48, a=7,\) and \(b=5\)

Find the solution of \(1 < \frac{1}{x} .\) (Hint: Will any negative values of \(x\) work?)

Solve each inequality and graph the solution on the number line. $$-1 \leq \frac{x+1}{3} \leq 3$$

Given that \(i=p r t,\) find \(r\) if \(i=120, p=500,\) and \(t=6\)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Pure 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.