The LinearUnivariate command solves a linear inequality with respect to one variable.

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

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

$\mathrm{LinearUnivariate}\left(2x<1\&comma;x\right)$

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

$\mathrm{LinearUnivariate}\left(2x<a\&comma;x\right)$

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

$\mathrm{LinearUnivariate}\left(ax\le 1\&comma;x\right)$

$\left\{\begin{array}{cc}\left\{x\le \frac{1}{a}\right\}& 0<a\\ \left\{\frac{1}{a}\le x\right\}& a<0\\ \left\{x\right\}& a=0\end{array}\right.$

$\mathrm{LinearUnivariate}\left(ax<1\&comma;x\right)$

$\left\{\begin{array}{cc}\left\{x<\frac{1}{a}\right\}& 0<a\\ \left\{\frac{1}{a}<x\right\}& a<0\\ \left\{x\right\}& a=0\end{array}\right.$

$\mathrm{LinearUnivariate}\left(ax+b<1\&comma;x\right)$

$\left\{\begin{array}{cc}\left\{x<-\frac{b-1}{a}\right\}& 0<a\\ \left\{-\frac{b-1}{a}<x\right\}& a<0\\ \left\{x\right\}& a=0\wedge b<1\\ \varnothing & a=0\wedge 1\le b\end{array}\right.$

$\mathrm{LinearUnivariate}\left(ax+b<1\&comma;x\right)\mathbf{assuming}0<a$

$\left\{x<-\frac{b-1}{a}\right\}$

$\mathrm{LinearUnivariate}\left(ax+b<1\&comma;x\right)\mathbf{assuming}1<b$

$\left\{\begin{array}{cc}\left\{x<-\frac{b-1}{a}\right\}& 0<a\\ \left\{-\frac{b-1}{a}<x\right\}& a<0\\ \varnothing & a=0\end{array}\right.$