Equations

An equation is a mathematical sentence, a relationship between numbers and/or symbols that says two expressions are of equal value.

Axioms of equality

For all real numbers a, b, and c, the following are some basic rules for using the equal sign.

• Reflexive axiom: a = a.
  
  Therefore, 4 = 4.
• Symmetric axiom: If a = b, then b = a.
  
  Therefore, if 2 + 3 = 5, then 5 = 2 + 3.
• Transitive axiom: If a = b and b = c, then a = c.
  
  Therefore, if 1 + 3 = 4 and 4 = 2 + 2, then 1 + 3 = 2 + 2.
• Additive axiom of equality: If a = b and c = d, then a + c = b + d.
  
  Therefore, if 1 + 1 = 2 and 3 + 3 = 6, then 1 + 1 + 3 + 3 = 2 + 6.
• Multiplicative axiom of equality: If a = b and c = d, then ac = bd.
  
  Therefore, if 1 = and 4 = , then .

Solving equations

Remember that an equation is like a balance scale with the equal sign (=) being the fulcrum, or center. Thus, if you do the same thing to each side of the equation (say, add 5 to each side), the equation will still be balanced.
In the same manner, you may subtract, multiply, or divide both sides of an equation by the same (nonzero) number, and the solution will not change. Sometimes you may have to use more than one step to solve for an unknown.

Literal equations

Literal equations have no numbers, only symbols (letters).

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By Muhammad Atif Saeed on 23:56. Filed under Mathandstat . Follow any responses to the RSS 2.0. Leave a response