X+4-х/3<2х/3

To solve the inequality \( x + 4 - \frac{x}{3} < \frac{2x}{3} \), we can follow these steps:

1. Combine like terms. First, let's eliminate the fraction by multiplying the entire inequality by 3 (the least common multiple of 3):

   \[ 3(x + 4) - x < 2x \]

   Simplifying this gives:

   \[ 3x + 12 - x < 2x \]

   Which simplifies to:

   \[ 2x + 12 < 2x \]

2. Subtract \( 2x \) from both sides:

   \[ 12 < 0 \]

This is a contradiction, which means that there are no values of \( x \) that satisfy the original inequality.

Thus, the solution set is the empty set, indicating there are no solutions.