Your question asks about "each inequalities" which is grammatically impossible since "each" implies singular whereas inequalities implies plural. Consequently it is not clear whether you mean "each inequality" or "each of a set of inequalities". In either case the set is called the feasible region, or the 2-dimensional solution set.
It is called the "soulltion set"
Equation: A statement that asserts that two mathematical expressions are equal in value. If this is true for all values of the variables involved then it is called an identity, and where it is only true for some values it is called a conditional equation. Inequality: A statement that uses the symbols > (greater than), < (less than), ≥ (greater than or equal to), ≤ ( less than or equal to) to indicate that one of the quantity is larger or smaller than another. An inequality holds for all values of the variables involved. If a statement that uses one of the symbols above holds only for some values of the variables involved then it is called an inequation. An inequality is comparable to an identity. If you'd want to put it into easier kid friendly words, an inequality is a statement where two sides of the inequality are not equal. Equations on the other hand, two sides should always be equal, no mater how messed up hard one side might look to you. Trust me I've been there.
If the "comparison symbol" is the equal sign, it is called an "equation". If the symbol is less than, greater than, less-than-or-equal, or greater-than-or-equal, it's called an "inequality".
A bivariate linear inequality.
It is called the DOMAIN!
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. If your question is not answered, please resubmit it, spelling out the symbols as "plus", "minus", "equals" etc. Also use ^ to indicate powers (x^2) or x-squared.In this case, you probably typed something like, "If a>b, then a-c > b-c". This would be called the subtraction property of inequality, and is one of the rules used to solve inequalities.
Statements in which the two sides are not equal are called inequalities.
That is called an inequality.
If by symbols you mean the abbreviations for element names like Aluminum's is Al. The symbols are called atomic symbols.