LinearUnivariate - Maple Help

SolveTools[Inequality]

 LinearUnivariate
 solve a linear inequality with respect to one variable

 Calling Sequence LinearUnivariate(ineq, var)

Parameters

 ineq - inequality var - variable name

Description

 • 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

Examples

 > $\mathrm{with}\left(\mathrm{SolveTools}\left[\mathrm{Inequality}\right]\right):$
 > $\mathrm{LinearUnivariate}\left(2x<1,x\right)$
 $\left\{{x}{<}\frac{{1}}{{2}}\right\}$ (1)
 > $\mathrm{LinearUnivariate}\left(2x
 $\left\{{x}{<}\frac{{a}}{{2}}\right\}$ (2)
 > $\mathrm{LinearUnivariate}\left(ax\le 1,x\right)$
 $\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\$ (3)
 > $\mathrm{LinearUnivariate}\left(ax<1,x\right)$
 $\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\$ (4)
 > $\mathrm{LinearUnivariate}\left(ax+b<1,x\right)$
 $\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\$ (5)
 > $\mathrm{LinearUnivariate}\left(ax+b<1,x\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{assuming}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}0
 $\left\{{x}{<}{-}\frac{{b}{-}{1}}{{a}}\right\}$ (6)
 > $\mathrm{LinearUnivariate}\left(ax+b<1,x\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{assuming}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}1
 $\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\$ (7)