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Chapter 1: Problem 70

Solve for the specified variable. (See Examples \(8-9)\) $$ E=I R \text { for } R $$

Short Answer

Expert verified
R = \frac{E}{I}

Step by step solution

01

Write the Given Equation

Begin by writing down the given equation: \[ E = I R \]
02

Identify the Variable to Solve For

We need to solve for the variable \( R \).
03

Isolate the Variable

To isolate \( R \), divide both sides of the equation by \( I \). This gives us: \[ R = \frac{E}{I} \]

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Key Concepts

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

variable isolation
Isolating the variable is the fundamental step in solving linear equations. It involves getting the variable you are solving for by itself on one side of the equation. In our example, we are solving for \( R \) in the equation \( E = IR \). We need to isolate \( R \). To do this, we divide both sides of the equation by \( I \), giving us \( R = \frac{E}{I} \). By isolating the variable, we transform the equation into a form where \( R \) is the subject of the formula. This step is pivotal because it simplifies the problem and leads us to the solution.
algebraic manipulation
Algebraic manipulation refers to the processes used to rearrange and simplify equations. This involves operations such as addition, subtraction, multiplication, and division to maintain the equality of both sides of the equation. It is crucial to perform the same operation on both sides to keep the equation balanced. For instance, in \( E = IR \), we performed an algebraic manipulation by dividing both sides by \( I \). This operation must be applied to the entire equation to correctly isolate \( R \). Understanding and applying these manipulations properly is essential for solving equations accurately and efficiently.
equation solving
Solving an equation means finding the value of the variable that makes the equation true. Let's break down our example step by step. First, we wrote down the given equation: \( E = IR \). Next, we identified the variable to solve for, which in this case is \( R \). Finally, we isolated \( R \) by dividing both sides by \( I \), resulting in \( R = \frac{E}{I} \). By following these steps, we solved the equation for the specified variable. This process can be applied to a wide range of equations, making it a standard technique in algebra.

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