## 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).