Applications of Linear Equations

Example 102.

If \(28\) less than five times a certain number is \(232\). What is the number?

\(5 x-28\)	Subtraction is built backwards, multiply the unknown by \(5\)
\(5 x-28=232\)	Is translates to equals
\(underline +28 \quad +28\)	Add \(28\) to both sides
\(\underline {5x=260}\)	The variable is multiplied by \(5\)
\( 5 \quad \quad 5\)	Divide both sides by \(5\)
\(x=52\)	The number is \(52\).

This same idea can be extended to a more involved problem as shown in the next example.