Linear inequalities in one variable
It is called the "soulltion set"
an inequality
A bivariate linear inequality.
Each linear equation is a line that divides the coordinate plane into three regions: one "above" the line, one "below" and the line itself. For a linear inequality, the corresponding equality divides the plane into two, with the line itself belonging to one or the other region depending on the nature of the inequality. A system of linear inequalities may define a polygonal region (a simplex) that satisfies ALL the inequalities. This area, if it exists, is called the feasible region and comprises all possible solutions of the linear inequalities. In linear programming, there will be an objective function which will restrict the feasible region to a vertex or an edge of simplex. There may also be a further constraint - integer programming - where the solution must comprise integers. In this case, the feasible region will comprise all the integer grid-ponits with the simplex.
Hieroglyphics
A mathematical sentence that compares expressions using symbols is called an inequality. Inequalities use symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to) to compare two values or expressions. For example, the inequality (3x + 2 > 5) indicates that the expression (3x + 2) is greater than 5 for certain values of (x). This allows for a range of solutions rather than a single definitive outcome.
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"
A mathematical sentence indicating that two quantities are not equal is called an inequality. It is typically expressed using symbols such as "≠" (not equal to), "<" (less than), or ">" (greater than). Inequalities can represent a range of values and are fundamental in various mathematical contexts, including algebra and calculus.
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.
A pair of inequalities joined by "and" is called a conjunction, while a pair of inequalities joined by "or" is called a disjunction.
The values or set of values that make an inequality or equation true are called solutions or roots. In the case of equations, these values satisfy the equation when substituted into it, while for inequalities, they make the inequality hold true. Finding these solutions is a fundamental aspect of algebra and helps in understanding the relationships between variables.
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.
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".
an inequality
It is called the DOMAIN!
A bivariate linear inequality.