Answer
$(-∞, -3]$
Work Step by Step
Plug the given conditions into an inequality. Put similar terms on either side and then find the least common denominator of all the terms to eliminate the fractions. Then simplify by isolating $x$.
$\frac{x}{2}+3\leq\frac{x}{3}+\frac{5}{2}$
$\frac{x}{2}+\frac{1}{2}\leq\frac{x}{3}$
$6(\frac{x}{2}+\frac{1}{2})\leq6(\frac{x}{3})$
$3x+3\leq2x$
$-3\geq x$
$x\leq-3$
$(-∞, -3]$
