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of an equation written with only one variable is the set of all values one can assign to that variable to make the equation a true statement.  Any one of those values is said to be a solution to the equation.

** To solve an equation means to find the solution set for that equation

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is a statement of equality between two numerical expressions.
* It is true if both numerical expressions are equivalent.  It is false otherwise.  True and false are called truth values.

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is either
*  A numerical symbol or a variable symbol, or
*  The result of placing previously generated algebraic expressions separated by one of the four operations +, -, *, / or as the base of an exponentiation.

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is a symbol that is a placeholder for a number.

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is a symbol that represents a specific number.
For example, 0, 1, 2, 3, 2/3, -3, -124.222, pi, e
All of these represent specific points on the number line.

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T1B:  Distributive Property of Arithmetic

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T1B:  Distributive Property of Arithmetic

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if a, b, and c are real numbers, then:
a*(b + c) = a*b + a*c

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T1B:  Associative Property of Addition and Multiplication

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T1B:  Associative Property of Addition and Multiplication

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if a, b, and c are real numbers, then:
(a + b) + c = a + (b + c)
and
(a*b)*c = a*(b*c)

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T1B:  Commutative Property of Addition and Multiplication

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T1B:  Commutative Property of Addition and Multiplication

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If a and b are real numbers, then:
a + b = b + a
and
a * b = b * a

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is the sum of the exponents of the variable symbols that appear in the monomial.

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Monomial:  a polynomial expression generated only using the multiplication operator.
Binomial:  the sum (or difference) of two monomials.
Trinomial:  the sum (or difference) of three monomials.
Polynomial:  the sum (or difference) of four or more monomials.

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is the degree of the monomial term with the highest degree.

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is an algebraic expression that contains only numerical symbols which evaluate to a single number.

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*  A numerical expression or a variable symbol, or
*  The result of placing two previously generated polynomial expressions separated either by addition or multiplication.
Formally:

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Given non-overlapping intervals on the real number line, a (real) piecewise linear function is a function from the union of the intervals on the real number line that is defined by (possibly different) linear functions on each interval.