Question

$-x+3\ \textgreater \ \:2x+1$ me ajudem a achar a resposta

Answer 1

$-x+3\ \textgreater \ 2x+1\quad :\quad \begin{bmatrix}\mathrm{Solucao:}\:&\:x\ \textless \ \frac{2}{3}\:\\ \:\mathrm{Decimal:}&\:x\ \textless \ 0.66667\dots \\ \mathrm{Notacao\:intervalo}&\:\left(-\infty \:,\:\frac{2}{3}\right)\end{bmatrix}$

Vamos resolver então.

$\mathrm{Subtrair\:}3\mathrm{\:de\:ambos\:os\:lados}$
$-x+3-3\ \textgreater \ 2x+1-3$
$\mathrm{Simplificar}$
$-x\ \textgreater \ 2x-2$
$\mathrm{Subtrair\:}2x\mathrm{\:de\:ambos\:os\:lados}$
$-x-2x\ \textgreater \ 2x-2-2x$
$\mathrm{Simplificar}$
$-3x\ \textgreater \ -2$
$Multiplicar\:ambos\:os\:lados\:por\:-1\:\left(inverte\:a\:desigualdade\right)$
$\left(-3x\right)\left(-1\right)\ \textless \ \left(-2\right)\left(-1\right)$
$\mathrm{Simplificar}$
$3x\ \textless \ 2$
$\mathrm{Dividir\:ambos\:os\:lados\:por\:}3$
$\frac{3x}{3}\ \textless \ \frac{2}{3}$
$\mathrm{Simplificar}$
$x\ \textless \ \frac{2}{3}$

Answer 2

$-x+3\ \textgreater \ 2x+1$
$-x-2x\ \textgreater \ 1-3$
$-3x\ \textgreater \ -2$
$3x\ \textless \ 2$
$x\ \textless \ \frac{2}{3}$

Solucão: X∈]-ifinito;2/3[