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Solving Linear Equations in One Variable

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The process of solving equations starts here with linear equations in one variable. Those are ones that can be made to look like


Practically every other type of equation we're going to look at throughout this course ultimately uses the methods developed here. If you like lists and procedures, these equations can be solved by following these steps:

  1. Multiply both sides to eliminate any fractions or decimals.
  2. Eliminate parentheses.
  3. Simplify each side by combining like terms.
  4. Get all variable terms on one side and all the numbers on the other side.
  5. Divide to get the variable by itself.
  6. Check your result.

If that seems like a lot, it sort of is, but you'll find that with just a little practice the process quickly becomes second nature.

Video Lectures


Solving linear equations in one variable is a core technique that's going to show up as part of the process for solving practically every other type of equation. (lecture slides)
There are a couple of special cases that show up when solving linear equations that you need to be aware of. In the first case, there are no solutions and, in the second, there are infinitely many solutions. (lecture slides)
Equations with fractions are another special case. You can solve the equations as is, finding common denominators as needed, or you can start by eliminating the fractions. (lecture slides)
Decimals aren't quite as challenging as fractions but they can be eliiminated from an equation using a very similar technique. (lecture slides)

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