Algebra

Revision as of 19:19, 29 February 2024 by Bromley (talk | contribs) (Created page with "== Solving equations == === Definitions === ==== Expression ==== = any form of showing a mathematical value * ex. the number 2 may be "expressed" as either "2" or "1+1" * more complex "expressions" involve variables, such as "2y -5 = 10" ** here, the value (expression) "10" can also be "expressed" as "2y - 5" === Equation === = a statement that uses an equal sign (=) * which means that the expressions on both side of the equal sign have the same value === Inverse...")
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Solving equations

Definitions

Expression

= any form of showing a mathematical value

  • ex. the number 2 may be "expressed" as either "2" or "1+1"
  • more complex "expressions" involve variables, such as "2y -5 = 10"
    • here, the value (expression) "10" can also be "expressed" as "2y - 5"

Equation

= a statement that uses an equal sign (=)

  • which means that the expressions on both side of the equal sign have the same value

Inverse Operation

= a method for isolating variables by adding or multiplying a value to both sides of an equation

  • the "inverse operation" reduces the value of the property on the side of the variable to 1 or 0
  • that way the variable becomes "isolated" on one side of the equation
  • ex.:
    • x + 3 = 8
  • the "inverse operation" adds -3 to both sides of the equation:
    • x + 3 - 3 = 8 - 3
  • which leaves us with
    • x + 0 = 5
    • x = 5

Property

  • = the rule that is applied to numbers in an equation
  • the property applied must be the same for both sides of the equation!
  • properties include
    • Addition property (or subtraction)
    • Multiplication property (or division)

Isolating the variable

  • Equations are solved by "isolating the variable"
    • which means "expressing" the unknown value by itself on one side of an equation
      • ex. to solve, "4 + x = 6" , we want to "isolate" x, so that we have "x = ___"

Properties of Equality

  • property = a rule
  • equality = that both sides of the equation (equal sign) have the same value