How do you combine numbers and symbols in an algebraic equation?
Working with variables and solving equations are often considered the basis of algebra. An equation is a mathematical sentence, a relationship between numbers and/or symbols.
For all real numbers a, b, and c, the following are some basic rules (axioms) for using the equal sign.
For all real numbers a, b, and c, the following are some basic rules (axioms) for using the equal sign.
Reflexive axiom: a = a.
Therefore, 4 = 4.
Symmetic 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: 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: If a = b and c = d, then ac = bd.
Therefore, if 1 = 2/2 and 4 = 8/2, then 1(4) = (2/2)(8/2).