We have learned how to solve linear equations with one unknown, and how to identify a linear equation in other types of equations. Here are some examples of equations we dealt with.

\[\begin{aligned}
&2x+3=5x-6 \quad\quad\quad &\dfrac{2x-3}{6x-5} = 3 \\
&\dfrac{2}{x+3}+3=\dfrac{5}{x+3}-6\quad\quad\quad &|2x+3|=|5x-6|=7\\
&2x^4+3=5x^4-6 \quad\quad\quad &\left(2x-3\right)\cdot\left(6x-5\right) = 0
\end{aligned}\]

We started with the formula for the transition from Fahrenheit to Celsius:\[C = \dfrac{5}{9}(F-32)\tiny,\] in which #C# indicates the temperature in degrees Celsius and #F# the temperature in degrees Fahrenheit. If we want to express #F# in #C#, we consider the formula as a linear equation with unknown #F# and known #C#, and we solve the equation just like we learned from the theory of reduction.

We only considered a small number of total possible applications.

Suggestions for continuing:

In the chapter Systems of linear equations we show how to expand this method of solving to bigger systems.

In the chapter Quadratic equations we will explain what happens when you allow the unknown to be a second-degree term.