 Linear inequality

A linear inequality compares a linear functional of a vector of unknowns with a constant, for example $a^{T}x\le b$ or $a^{T}x<b$ over the real numbers. For $a\ne 0$, its solution set is a closed or open half-space, respectively. The inequality $x+y\le 1$ allows all points on one side of the line $x+y=1$, including the line. Multiplication by a negative real number reverses the inequality, so $x\ge 1$ is equivalently $-x\le -1$.

A linear inequality is a mathematical expression that represents a relationship between two values or expressions that is not necessarily equal, but rather indicates that one is greater than, less than, greater than or equal to, or less than or equal to the other. Linear inequalities involve linear expressions, which are polynomials of degree one.