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Solving Linear Equations

An equation is a statement indicating that two expressions are equal. In the case of a linear equation, it can be simplified into the form ax = b where a and b are real numbers, with a ≠ 0.

Solving a Linear Equation

To solve a linear equation, you have to isolate for the variable by doing the following steps:

  • Expand (if applicable).
  • Group like terms (if applicable).
  • Rearrange  so that all terms with the variable in them are on one side of the equation while all the terms without the variable in them (i.e., just number terms) are on the other side (i.e., rearrange into the form ax = b [to do this, you're just adding/subtracting terms from both sides]).
  • Divide by the coefficient of the variable to solve for the variable (i.e., once you've got ax = b, divide both sides by a to solve for x).

Example: Solve the equation 3x - 12 = 0

Solution:

3x - 12 = 0

        3x = 0 + 12

        3x = 12

           x = 4

Example: Solve the equation 3x + 4 = 7x - 6 - 6x

Solution:

3x + 4 = 7x - 6 - 6x

3x + 4 = x - 6

  3x - x = - 6 - 4

       2x = -10

          x = -5

Example:

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