Algebra Explained

How do you simplify an algebraic equation?

The best way to simplify an equation is to combine like terms, which makes the equation simpler to solve. Numbers may be combined, as well as any terms with the same variable.

Terms can be combined either by adding or subtracting variables of the same kind. One can also use multiplication and division to simplify an equation by multiplying or dividing each side by the same number (except 0). The following are some examples:

  • Add the like terms: 4x + 3x = 14, simplifies to 7x = 14.
  • The equation 4 + 8x + 10 - 4x - 2 = 20 can be simplified by combining the like terms, which gives the simplified result 12 + 4x = 20.
  • If necessary, do a combination of addition, subtraction, multiplication, or division. For example, the equation 2x - 2 = 4x + 3, simplifies to 2x = 4x + 5 (by adding 2 to both sides); then subtract 2x from both sides, simplifying to 0 = 2x + 5. (Note: Since subtracting any number is the same as adding its negative, it is often more helpful to replace subtractions with additions of a negative number.) Finally, subtract 5 from both sides (or 2x = -5) divide both sides by 2, resulting in the solution of x = -5/2 (or -2.5).
  • To simplify expressions raised to a power, certain rules should be followed. For example, for (x + 3)2 - 4x, square x + 3, or (x + 3)(x + 3), first squaring the first term (x squared equals x2), then the second (3 squared equals 9), then multiply and add the inner and outer terms together (3x + 3x = 6x). By combining like terms, the entire equation results in the simplified expression x2 + 6x + 9 - 4x, which finally equals x2 + 2x + 9.


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