Answer
The solution set is $\{-1\}$.
Work Step by Step
Multiply both sides of the given equation by the least common denominator of the fractions (which is $10$) to clear fractions.
$10\left (\frac{3x-1}{5}+\frac{x+2}{2}\right )=10\left (-\frac{3}{10} \right )$
Use the distributive property .
$10\left (\frac{3x-1}{5}\right )+10 \left (\frac{x+2}{2}\right )=10\left (-\frac{3}{10} \right )$
Simplify.
$2(3x-1)+5 (x+2 )=-3$
Use the distributive property and clear the parentheses.
$6x-2+5x+10=-3$
Add like terms.
$11x+8=-3$
Subtract $8$ from both sides.
$11x+8-8=-3-8$
Add like terms.
$11x=-11$
Divide both sides by $11$.
$\frac{11x}{11}=\frac{-11}{11}$
Simplify.
$x=-1$.
