Question

el conjunto solucion para la inecuacion 3/5(x-5)+2/3(x-3)>-6

Answer 1

$\frac{3}{5}\left(x-5\right)+\frac{2}{3}\left(x-3\right)\ \textgreater \ -6$
$\mathrm{Encontrar\:el\:minimo\:comun\:multiplo\:de\:}5,\:3:\quad 15$
$\mathrm{Multiplicar\:por\:el\:minimo\:comun\:multiplo=}15:$
$\frac{3}{5}\left(x-5\right)\cdot \:(15)+\frac{2}{3}\left(x-3\right)\cdot \:(15)\ \textgreater \ -6\cdot \:(15)$
$9\left(x-5\right)+10\left(x-3\right)\ \textgreater \ -90$
$\mathrm{Poner\:los\:parentesis\:utilizando}:\quad \:a\left(b-c\right)=ab-ac$
$9x-45+10x-30\ \textgreater \ -90$
$19x-75\ \textgreater \ -90$
$\mathrm{Sumar\:}75\mathrm{\:a\:ambos\:lados}:$
$19x-75+75\ \textgreater \ -90+75$
$19x\ \textgreater \ -15$
$\mathrm{Dividir\:ambos\:lados\:entre\:}19:$
$\frac{19x}{19}\ \textgreater \ \frac{-15}{19}$
$x\ \textgreater \ -\frac{15}{19}$
$\begin{bmatrix}\mathrm{Solucion:}\:&\:x\ \textgreater \ -\frac{15}{19}\:\\ \:\mathrm{Decimal:}&\:x\ \textgreater \ -0.78947\dots \\ \mathrm{Notacion\:intervalo}&\:\left(-\frac{15}{19},\:\infty \:\right)\end{bmatrix}$