Question

encuentra la solucion de las inecuaciones
a)1-5x/4 - 2 4 3x/5 < 1/2
b)-2 3x/5 6-4x/4 1/2>0
c)1 -2x-5/6 1-4x/2 - x-1/3<0

Answer 1

$a) 1- \frac{5}{4}x - \frac{243}{5}\ \textless \ \frac{1}{2} \\ \\ - \frac{5}{4}x - \frac{243}{5}\ \textless \ \frac{1}{2}-1 \\ \\ - \frac{5*5}{4*5}x - \frac{243*4}{5*4}\ \textless \ \frac{1}{2}- \frac{2}{2} \\ \\- \frac{25}{20}x - \frac{972}{20}\ \textless \ \frac{1-2}{2} \\ \\ \frac{-25-972}{20}x\ \textless \ -\frac{1}{2} \\ \\ - \frac{997}{20}x\ \textless \ -\frac{1}{2} \\ \\ x\ \textless \ - \frac{1}{2}: - \frac{997}{20} \\ \\ x\ \textless \ - \frac{10}{997}\to x \ pertenece \ a (-\infty; - \frac{10}{997})$

$b) -2 \frac{3}{5}x+6- \frac{4x}{4}+ \frac{1}{2}\ \textgreater \ 0 \\ \\ - \frac{13}{5}x- \frac{4x}{4}\ \textgreater \ - \frac{1}{2} -6\\ \\ - \frac{52-20}{20}x\ \textgreater \ -\frac{13}{6} \\ \\ - \frac{72}{20}x\ \textgreater \ -\frac{13}{6} \\ \\ x\ \textless \ -\frac{13}{6}: - \frac{72}{20} \to x\ \textless \ + \frac{260}{432}\to x \ \textless \ \frac{65}{108}$

 $c)1-2x- \frac{5}{6}+1- \frac{4}{2}x-x- \frac{1}{3}\ \textless \ 0 \\ \\ -2x- \frac{4}{2}x-x\ \textless \ -1+ \frac{5}{6}-1+ \frac{1}{3} \\ \\ - \frac{7}{2}x\ \textless \ -2+ \frac{7}{6} \\ \\ x\ \textgreater \ - \frac{5}{6}: - \frac{7}{2}\to x\ \textgreater \ + \frac{5}{21}$

Espero que te sirva, salu2!!!!