Solve x+1=2/3x algebraically

the way you typed it ...

multiply each term by 3

3x + 3 = 2x
x = -3

if you meant
x + 1 = 2/(3x), then mulltiply each term by 3x
3x^2 + 3x = 2
3x^2 + 3x - 2 = 0
use the quadratic formula to solve for x