Problem 73 - Introductory Algebra for College Students

Question

Explain what it means to solve a formula for a variable.

Step-by-Step Solution

Answer

Solving a formula for a variable refers to the process of isolating the variable (making it the subject) using mathematical operations, so it can be expressed as a function of the other variables.

Step 1: Understanding the concept of a variable

A variable in a formula or an equation often represents an unknown quantity. It can also represent an arbitrary but specific quantity in the scope of the given problem.

Step 2: Interpretation of solving a formula

Solving a formula for a variable means manipulating the formula in such a way that we isolate the desired variable on one side of the equation. This variable can then be expressed as a function of the other variables in the formula.

Step 3: Process of solving a formula

This process of solving involves applying mathematical operations such as addition, subtraction, multiplication, and division to transform the formula. All operations should be balanced, meaning whatever operation is performed on one side should be done to the other side as well. This maintains the 'equality' in equations.

Step 4: Example of solving a formula for a specified variable

Consider an example, suppose the given formula is \(2a = b + c\) and the task is to solve for \(a\). To isolate \(a\), divide both sides of the equation by 2, resulting in \(a = (b + c) / 2\). Here, \(a\) is now expressed in terms of \(b\) and \(c\).