The LinearUnivariateSystem command solves a system of linear inequalities with respect to one variable.

The LinearUnivariateSystem command returns a set describing the interval of possible values of the variable or a piecewise function of such sets depending on parameters

$\mathrm{with}\left(\mathrm{SolveTools}\left[\mathrm{Inequality}\right]\right)\:$

$\mathrm{LinearUnivariateSystem}\left(\left\{0<x+1\&comma;0<2x-1\right\}\&comma;x\right)$

$\left\{\frac{1}{2}<x\right\}$

$\mathrm{LinearUnivariateSystem}\left(\left\{0<x+1\&comma;2x-1<0\right\}\&comma;x\right)$

$\left\{\mathrm{-1}<x\&comma;x<\frac{1}{2}\right\}$

$\mathrm{LinearUnivariateSystem}\left(\left\{x+1<0\&comma;2x-1<0\right\}\&comma;x\right)$

$\left\{x<\mathrm{-1}\right\}$

$\mathrm{LinearUnivariateSystem}\left(\left\{0<2x-1\&comma;x+1<0\right\}\&comma;x\right)$

$\varnothing$

$\mathrm{LinearUnivariateSystem}\left(\left\{0<2x-1\&comma;x+a<0\right\}\&comma;x\right)$

$\left\{\begin{array}{cc}\left\{\frac{1}{2}<x\&comma;x<-a\right\}& a<-\frac{1}{2}\\ \varnothing & \mathrm{otherwise}\end{array}\right.$

$\mathrm{LinearUnivariateSystem}\left(\left\{0\le 2x-b\&comma;2x+a\le 0\right\}\&comma;x\right)$

$\left\{\begin{array}{cc}\left\{x\le -\frac{a}{2}\&comma;\frac{b}{2}\le x\right\}& a\le -b\\ \varnothing & \mathrm{otherwise}\end{array}\right.$

$\mathrm{LinearUnivariateSystem}\left(\left\{0\le 2x-b\&comma;ax+2\le 0\right\}\&comma;x\right)$

$\left\{\begin{array}{cc}\left\{x\le -\frac{2}{a}\&comma;\frac{b}{2}\le x\right\}& 0<a\wedge \frac{b}{2}\le -\frac{2}{a}\\ \left\{-\frac{2}{a}\le x\right\}& a<0\wedge \frac{b}{2}<-\frac{2}{a}\\ \left\{\frac{b}{2}\le x\right\}& a<0\wedge -\frac{2}{a}\le \frac{b}{2}\\ \varnothing & a=0\\ \varnothing & \mathrm{otherwise}\end{array}\right.$

$\mathrm{LinearUnivariateSystem}\left(\left\{ax+b<0\&comma;0\le cx+d\right\}\&comma;x\right)$

$\left\{\begin{array}{cc}\left\{x\le -\frac{d}{c}\right\}& 0<a\wedge c<0\wedge -\frac{d}{c}<-\frac{b}{a}\\ \left\{x<-\frac{b}{a}\right\}& 0<a\wedge c<0\wedge -\frac{b}{a}\le -\frac{d}{c}\\ \left\{-\frac{d}{c}\le x\&comma;x<-\frac{b}{a}\right\}& 0<a\wedge 0<c\wedge -\frac{d}{c}<-\frac{b}{a}\\ \left\{x<-\frac{b}{a}\right\}& 0<a\wedge c=0\wedge 0\le d\\ \varnothing & 0<a\wedge c=0\wedge d<0\\ \left\{x\le -\frac{d}{c}\&comma;-\frac{b}{a}<x\right\}& a<0\wedge c<0\wedge -\frac{b}{a}<-\frac{d}{c}\\ \left\{-\frac{d}{c}\le x\right\}& a<0\wedge 0<c\wedge -\frac{b}{a}<-\frac{d}{c}\\ \left\{-\frac{b}{a}<x\right\}& a<0\wedge 0<c\wedge -\frac{d}{c}\le -\frac{b}{a}\\ \left\{-\frac{b}{a}<x\right\}& a<0\wedge c=0\wedge 0\le d\\ \varnothing & a<0\wedge c=0\wedge d<0\\ \left\{x\le -\frac{d}{c}\right\}& a=0\wedge b<0\wedge c<0\\ \left\{-\frac{d}{c}\le x\right\}& a=0\wedge b<0\wedge 0<c\\ \left\{x\right\}& a=0\wedge b<0\wedge c=0\wedge 0\le d\\ \varnothing & a=0\wedge b<0\wedge c=0\wedge d<0\\ \varnothing & a=0\wedge 0\le b\end{array}\right.$