Problem 84 Solve each formula for the speci... [FREE SOLUTION]

91影视

Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 2: Problem 84

Solve each formula for the specified variable. $$ A=p+p r t \text { for } r $$

Short Answer

Expert verified

r = \frac{A - p}{pt}

Step by step solution

Write down the formula

The given formula is \[ A = p + prt \]. We need to solve for the variable $ r $.

Isolate the term with r

Subtract $ p $ from both sides of the equation to isolate the term containing $ r $: \[ A - p = prt \].

Solve for r

Divide both sides of the equation by $ pt $ to solve for $ r $: \[ r = \frac{A - p}{pt} \].

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Key Concepts

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

isolate variable

Isolating the variable is a crucial step in solving equations. It means moving the variable you are solving for to one side of the equation and everything else to the other. In our exercise, we are solving for the variable $ r $ in the equation $ A = p + prt $. The first step is isolating the term with $ r $ by subtracting $ p $ from both sides. This gives us $ A - p = prt $. Now, we have an equation where the term with the variable we want, $ r $, is isolated on one side.

algebraic manipulation

Algebraic manipulation refers to the steps we take to simplify or rearrange an equation. These steps can include addition, subtraction, multiplication, division, and factoring. In our example, after isolating the term with $ r $, we further manipulate the equation to solve for $ r $. We do this by dividing both sides of the equation by $ pt $: $ r = \frac{A - p}{pt} $. Algebraic manipulation is a powerful tool because it allows us to transform complex equations into simpler forms that are easier to solve.

solving for a variable

Solving for a variable means finding the value of that variable in terms of the other variables and constants in the equation. In our exercise, we solved for $ r $ in terms of $ A $, $ p $, and $ t $. By isolating and manipulating the equation step-by-step, we determined that $ r = \frac{A - p}{pt} $. This means that given any values for $ A $, $ p $, and $ t $, we can find the specific value of $ r $. The process of solving for a variable helps us understand the relationship between different variables and how they affect one another.

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91影视

Solve each formula for the specified variable. $$ A=p+p r t \text { for } r $$

Short Answer

Step by step solution

Write down the formula

Isolate the term with r

Solve for r

Key Concepts

isolate variable

algebraic manipulation

solving for a variable

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