= Linear inequality
{title2=$a^Tx\leq b$}
{wiki}
A linear inequality compares a <linear functional> of a <vector> of unknowns with a constant, for example $a^Tx\leq b$ or $a^Tx<b$ over the <real numbers>. For $a\ne0$, its <solution set> is a closed or open <half-space>, respectively. The inequality $x+y\leq1$ 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 $x\geq1$ is equivalently $-x\leq-1$.
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