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Chapter 2: Problem 73

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

Short Answer

Expert verified
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 by step solution

01

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.
02

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.
03

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.
04

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 \(c\).

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Most popular questions from this chapter

The bar graph shows average yearly earnings in the United States for people with a college education, by final degree earned. Exercises \(23-24\) are based on the data displayed by the graph. (GRAPH CANNOT COPY) The average yearly salary of an American whose final degree is a doctorate is 39 dollars thousand less than twice that of an American whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn 126 dollars thousand. Find the average yearly salary of Americans with each of these final degrees.

Solve each inequality. Use a calculator to help with the arithmetic. \(1.45-7.23 x>-1.442\)

A rectangular field is four times as long as it is wide. If the perimeter of the field is 500 yards, what are the field's dimensions?

Simplify: \(\left[3\left(12 \div 2^{2}-3\right)^{2}\right]^{2}\) (Section \(1.8,\) Example 8 )

Solve for \(x: \frac{x}{2}+7=13-\frac{x}{4}\) (Section \(2.3,\) Example 4 )
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