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Solving Equations

In: Basic Mathematics for Biochemists

Author

Listed:
  • Athel Cornish-Bowden

    (University of Birmingham)

Abstract

An equation such as $$4+x=8-2x$$ contains only one unknown quantity, x, and is linear, because it contains no terms higher than the first power of x. Although it is easy to solve such an equation it is nonetheless useful to examine the processes involved as they illustrate in a simple way the methods to be used for solving more difficult equations. The first essential is to rearrange the equation so that terms of the same type, in this case constants and terms in x, are brought together. It is often convenient to collect all constants on the right-hand side and other terms on the left-hand side. This may be done by use of the principle that we can apply any operation we like to an equation (other than multiplying or dividing by zero) provided that we apply it identically to both sides. So, for example, we can subtract 4 from both sides of the above equation and add 2x to both sides: $$4+x-4+2x=8-2x-4+2x$$ i.e. $$3x=4$$ The operation of subtracting, for example, 4 from both sides is clearly equivalent to ‘bringing it from one side to the other of the equation and changing its sign’. Although this is a convenient and proper way of carrying out the operation one should realize that it is no more than an example of applying the same operation to both sides of an equation.

Suggested Citation

  • Athel Cornish-Bowden, 1981. "Solving Equations," Springer Books, in: Basic Mathematics for Biochemists, chapter 5, pages 91-116, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-6523-5_5
    DOI: 10.1007/978-94-011-6523-5_5
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