Applications of Linear Equations

Objective: Solve number and geometry problems by creating and solving a linear equation.

Word problems can be tricky. Often it takes a bit of practice to convert the English sentence into a mathematical sentence. This is what we will focus on here with some basic number problems, geometry problems, and parts problems.

A few important phrases are described below that can give us clues for how to set up a problem.

• A number (or unknown, a value, etc) often becomes our variable
• Is (or other forms of is: was, will be, are, etc) often represents equals (=) \(x\) is 5 becomes \(x =5\)
• More than often represents addition and is usually built backwards, writing the second part plus the first
  Three more than a number becomes \(x + 3\)
• Less than often represents subtraction and is usually built backwards as well, writing the second part minus the first
  Four less than a number becomes \(x − 4\)

Using these key phrases we can take a number problem and set up and equation and solve.

Source: Tyler Wallace, http://www.wallace.ccfaculty.org/book/Beginning_and_Intermediate_Algebra.pdf
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