Question

what is the solution set of the inequation 3/(x) +2 ≥1​

Answer 1

$\textbf{Given:}$

$\mathsf{\dfrac{3}{x}+2\,\geq\,1}$

$\textbf{To find:}$

$\textsf{Solution set of the given inequality}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{\dfrac{3}{x}+2\,\geq\,1}$

$\mathsf{\dfrac{3}{x}\,\geq\,1-2}$

$\mathsf{\dfrac{3}{x}\,\geq\,-1}$

$\textsf{Taking reciprocals,}$

$\mathsf{\dfrac{x}{3}\,\leq\,-1}$

$\mathsf{x\,\leq\,-3}$

$\implies\textsf{Any real number less than or equal to -3 will}$

$\textsf{satisfy the given inequality}$

$\therefore\mathsf{Solution\;set\;is\;(-\infty,-3]}$

Answer 2

$\textbf\red{Given:}$

$\mathsf{\dfrac{3}{x}+2\,\geq\,1}$

$\textbf\red{To find:}$

$\textsf{Solution set of the given inequality}$

$\textbf\red{Solution:}$

$\textsf{Consider,}$

$\mathsf{\dfrac{3}{x}+2\,\geq\,1}$

$\mathsf{\dfrac{3}{x}\,\geq\,1-2}$

$\mathsf{\dfrac{3}{x}\,\geq\,-1}$

$\textsf\red{Taking reciprocals,}$

$\mathsf{\dfrac{x}{3}\,\leq\,-1}$

$\mathsf{x\,\leq\,-3}$

$\implies\textsf{Any real number less than or equal to -3 will}$

$\textsf{satisfy the given inequality}$

$\therefore\mathsf\red{Solution\;set\;is\;(-\infty,-3]}$