Question

Solve : $-x+3\ \textgreater \ \:2x+1$

Answer 1

$-x+3>2x+1$

$\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}$

$-x+3-3>2x+1-3$

$\mathrm{Simplify}$

$-x>2x-2$

$\mathrm{Subtract\:}2x\mathrm{\:from\:both\:sides}$

$-x-2x>2x-2-2x$

$\mathrm{Simplify}$

$-3x>-2$

$\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}$

$\left(-3x\right)\left(-1\right)<\left(-2\right)\left(-1\right)$

$\mathrm{Simplify}$

$3x<2$

$\mathrm{Divide\:both\:sides\:by\:}3$

$\frac{3x}{3}<\frac{2}{3}$

$\mathrm{Simplify}$

$x<\frac{2}{3}$