How Do You Write Linear Equations From Word Problems?

To write linear equations from word problems, the student must first decide which quantities to assign variables to, and then decide what operations must be performed in order to solve the problem. For example, the unknown variable typically gets an assignation of x, and it must be determined whether addition, subtraction, multiplication, division or a combination of these is required.

Making sentences out of the problem before determining variables can help. For example, if a problem reads, "45 less than 3 times a number is equal to that number. Find the number," sentences should be written that say:

  • 45 is less than 3 times a number.
  • Let x be that number.

From there, a person can begin to solve in equation form. While this is a simple word problem, the steps are always the same. The problem should now be written in equation form:

  • 45 less than 3 times a number equates to 3x - 45. "Less than" denotes subtraction, and "times" denotes multiplication. Note that the multiplication is first.
  • Find the number equates to = x. Now the equation reads 3x - 45 = x. The variable x is used both times, and now must be isolated to one side to solve the problem.

The student should always look for words like "less than" and "times" to figure out what type of operation must be performed in order to solve the problem. These are referred to as "keywords."