2.3 Algebraic notation

Instead of using English words, we write algebra using mathematical notation:

  • x+2 means, “the sum of x and 2″, or alternatively, “x increased by 2″. Both refer to the same formula.
  • x-2 means “the difference between x and 2″, or alternatively, “x decreased by 2″. Both refer to the same formula.
  • 2x means “the product of 2 and x

A term is a combination of numbers and variables, involving only multiplication or division (and NOT addition or subtraction).

Examples of terms may be 2x, 3xy, 5x/y. As is evident, no plus or minus sign is present!

By convention, we write:

  • Numbers before the variables. This is why we write 2x, and not x2
  • Variables in alphabetical order. This is why we write xyz and not yzx
  • x instead of 1x. You can leave out the 1

When we use variables, the variables can take on any value. For example, when we write “2xy“, the x and y can refer to -10, -9.999, 5, 20, etc… absolutely any value! However, if you’ve been given more information, such as that x is 2 and y is 3, you can determine its single value, by substituting, i.e. 2*2*3=12. This process of replacing a variable with a number is known as substitution.

Word questions make algebra more difficult. For example, if I consistently see Mandy 5 times a month, how many times will I see her in x months? Well, that would be 5x


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