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How to Combine Like Terms & Rational Numbers

The purpose of simple equations containing one variable and numbers is to isolate that variable on one side of the equation to provide an answer of its value. Algebra is used to isolate the variables, applying the opposite operations of terms that need to be canceled out and moved to the other side. The equation can also be simplified if there are like terms that can be combined.

Instructions

- 1
  Solve a linear equation by combining like terms then using algebraic opposites to move terms away from the variable. Eliminate a rational number, or number that can be converted to fraction form, that is multiplied by the variable by converting it to fraction form then multiplying its inverse to both sides.
- 2
  Solve the equation:
  
  x + 0.5x + 3 = 5 + 4
  
  Combine the like terms on the left side of the equation:
  
  1.5x + 3 = 5 + 4
  
  Combine the like terms on the right side of the equation:
  
  1.5x + 3 = 9
  
  Subtract 3 from both sides to isolate the variable term:
  
  1.5x = 6
- 3
  Convert 1.5 to its fractional form:
  
  (3/2)x = 6
  
  Multiply both sides by the inverse fraction:
  
  (2/3) * (3/2)x = 6 * (2/3) becomes x = 12/3 or x = 4

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