your answer was correct!
first, you simplify the fractions and rewrite the equation. after, you add your y-intercept/b/(-17/6) to both sides. lastly, you kill the fraction in front of x (1/3) and multiply the whole equation by the reciprocal (opposite of fraction which is 3)
1/3x-17/6=-19/18
+17/6 +17/6
(1/3x=19/18)(3)
x=19/6 OR 3 1/6