Question

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

solve it

Answer 1

Answer:

tex]-x+3\ \textgreater \ \:2x+1[/tex]

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Answer 2

$-x+3>2x+1\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<\frac{2}{3}\:\\ \:\mathrm{Decimal:}&\:x<0.66666\dots \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\frac{2}{3}\right)\end{bmatrix}$

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

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

$\mathrm{Simplify}$

$-x>2x-2$

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

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

$\mathrm{Simplify}$

$-3x>-2$

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

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

$\mathrm{Simplify}$

$3x<2$