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Solving Literal Equations

A literal equation is an equation with more than one variable. Formulas can be considered literal equations. To solve a literal equation, use inverse operations and the Properties of Equality to isolate the variable of interest.
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Exercise

Solve for

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Solution
Notice that the equation above has many different variables. However, is the variable of interest. To isolate we need to move and to the right-hand side of the equation. Recall that only like terms can be combined.
Solved for the equation is
Concept

Rearranging Formulas

Sometimes, rearranging a formula so that a different variable is highlighted, can make solving a problem easier. The same approach as above can be followed to isolate a variable of interest.
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Exercise

To convert temperatures in Fahrenheit, to temperatures in Celsius, the following formula can be used. Solve the formula for Then use the resultant formula to convert Fahrenheit to Celsius. Round to the nearest degree.

Show Solution
Solution
In the given formula, is the variable of interest. To isolate we can move and to the left-hand side using inverse operations.
Thus, the formula we can use to convert degrees Fahrenheit to Celsius is Let's use this to find the equivalent of Fahrenheit in To begin, we'll substitute
Thus, Fahrenheit is approximately equivalent to Celsius.
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