# Solving Literal Equations

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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.
Exercise

Solve $Ax+By=C$ for $x.$

Solution
Notice that the equation above has many different variables. However, $x$ is the variable of interest. To isolate $x,$ we need to move $By$ and $A$ to the right-hand side of the equation. Recall that only like terms can be combined.
$Ax+By=C$
$Ax+By-By=C-By$
$Ax=C-By$
$\dfrac{Ax}{A}=\dfrac{C-By}{A}$
$x = \dfrac{C-By}{A}$
Solved for $x,$ the equation is $x = \dfrac{C-By}{A}.$
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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.
Exercise

To convert temperatures in Fahrenheit, $F,$ to temperatures in Celsius, $C,$ the following formula can be used. $F=\frac{9}{5}C+32$ Solve the formula for $C.$ Then use the resultant formula to convert $98 ^\circ$ Fahrenheit to Celsius. Round to the nearest degree.

Solution
In the given formula, $C$ is the variable of interest. To isolate $C,$ we can move $32$ and $\frac{9}{5}$ to the left-hand side using inverse operations.
$F=\dfrac{9}{5}C+32$
$F-32=\dfrac{9}{5}C$
$F-32=\dfrac{9C}{5}$
$5(F-32) = 9C$
$\dfrac{5(F-32)}{9}=C$
$C=\dfrac{5(F-32)}{9}$
Thus, the formula we can use to convert degrees Fahrenheit to Celsius is $C=\frac{5(F-32)}{9}.$ Let's use this to find the equivalent of $98 ^\circ$ Fahrenheit in $^\circ \text{Celsius}.$ To begin, we'll substitute $F=98.$
$C=\dfrac{5(F-32)}{9}$
$C=\dfrac{5({\color{#0000FF}{98}}-32)}{9}$
$C=\dfrac{5 \cdot 66}{9}$
$C=\dfrac{330}{9}$
$C=36.66\ldots$
$C=37$
Thus, $98 ^\circ$ Fahrenheit is approximately equivalent to $37 ^\circ$ Celsius.
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