Problem 74 Solve each equation for the spec... [FREE SOLUTION]

Chapter 5: Problem 74

Solve each equation for the specified variable. $$ P=k R+R-u \text { for } R $$

Short Answer

Expert verified

R = \frac{P + u}{k + 1}

Step by step solution

Isolate the terms with R

Start by grouping the terms that contain the variable R on one side of the equation. The given equation is P = kR + R - u. Add u to both sides to isolate the terms with R: P + u = kR + R.

Factor out R

Now that you have grouped the R terms together, factor out R from the right-hand side: P + u = R(k + 1).

Solve for R

Finally, isolate R by dividing both sides of the equation by k + 1: P + u = k + 1 That鈥檚 the final solution for equation.

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Key Concepts

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

Isolation of Variables

When solving equations, the first key step is often to isolate the variable you are solving for. In our exercise, we need to solve for $ R $.
This means we want $ R $ alone on one side of the equation.
We started with: $ P = kR + R - u $.
To isolate terms with $ R $ on one side, we need to add $ u $ to both sides, resulting in: $ P + u = kR + R $.
This process helps focus on the terms involving $ R $, paving the way for easier manipulation later.

Factoring

Factoring is another crucial step in solving equations. Once we have isolated the terms with our variable, we factor it out.
After isolating $ P + u = kR + R $, we can see $ R $ is a common factor on the right-hand side.
We can factor out $ R $ as follows: $ P + u = R(k + 1) $.
Factoring simplifies the equation, making it easier to solve for the desired variable.

Linear Equations

Linear equations like $ P = kR + R - u $ are equations where the variable, $ R $, only appears to the first power. This means there's no $ R^2, R^3 $, or any higher powers of $ R $.
Such equations often allow for straightforward manipulation and solution.
They can typically be solved through basic algebraic operations such as adding, subtracting, factoring, and dividing.

Variable Manipulation

Variable manipulation refers to the various algebraic techniques used to simplify and solve equations.
These include operations such as adding or subtracting terms from both sides of an equation, factoring out common terms, and dividing or multiplying by coefficients.
In our example, after factoring out $ R $, we need to isolate $ R $ further by dividing both sides by $ k + 1 $:
$ R = \frac{P + u}{k + 1} $.
Manipulating variables step-by-step helps us arrive at the solution efficiently and accurately.

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91影视

Solve each equation for the specified variable. $$ P=k R+R-u \text { for } R $$

Short Answer

Step by step solution

Isolate the terms with R

Factor out R

Solve for R

Key Concepts

Isolation of Variables

Factoring

Linear Equations

Variable Manipulation

One App. One Place for Learning.

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