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Chapter 1: Problem 77

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

Short Answer

Expert verified
Solving a formula for a variable means to isolate that variable on one side of the equation while other variables present in the formula are on the other side.

Step by step solution

01

Understanding the terms

First of all, it is essential to clarify what is meant by a 'formula', and a 'variable'. A formula is a rule or principle expressed in algebraic terms, while a variable is a letter or symbol which represents a number.
02

Solving a formula

To solve a formula for a certain variable means to isolate that variable on one side of the equation. This process includes performing reverse operations to eliminate other variables and constants from that side of the formula, making the variable the subject of the formula. This would mean applying rules of arithmetic including addition, subtraction, multiplication, division and possibly others depending on the complexity of the formula.
03

Explaining with an Example

As an example, if given the formula \(F = ma\), 'solve for \(a\)'. That means we want to isolate \(a\). In this formula, \(F\) is the force, \(m\) is mass, and \(a\) is acceleration. We want to get the acceleration \(a\) by itself on one side of the equation. So in this case, we divide both sides by \(m\) to solve for \(a\). Then we get \(a=F/m\) as the result. \(a\) is now isolated, and this is expressed in terms of \(F\) and \(m\).

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Most popular questions from this chapter

The formula $$1-\frac{1}{4^{x}+26}$$ models the percentage of U.S. households with an interfaith marriage, \(I, x\) years after \(1988 .\) The formula $$N-\frac{1}{4} x+6$$ models the percentage of U.S households in which a person of faith is married to someone with no religion, \(N, x\) years after \(\overline{l 9} 88\). Use these models to solve. a. In which years will more than \(34 \%\) of U.S. households. have an interfaith marriage? b. In which years will more than \(15 \%\) of U.S. households have a person of faith married to someone with no religion? c. Based on your answers to parts (a) and (b), in which years will more than \(34 \%\) of households have an interfaith marriage and more than \(15 \%\) have a faith/no religion marriage? d. Based on your answers to parts (a) and (b), in which years will more than \(34 \%\) of households have an interfaith marriage or more than \(15 \%\) have a faith/no religion marriage?

Solve compound inequality. \(3 \leq 4 x-3<19\)

Solve absolute value inequality. \(4<|2-x|\)

Solve absolute value inequality. \(|3(x-1)+2| \leq 20\)

Describe the solution set of \(|x|>-4\).
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