a) \( x+4-\frac{x}{3}<\frac{2 x}{9} \);

To solve the inequality \( x + 4 - \frac{x}{3} < \frac{2x}{9} \), first, eliminate fractions by finding a common denominator, which is 9 in this case. Multiply each term by 9 to clear the fractions, yielding: \[ 9(x + 4) - 3x < 2x. \] This simplifies to: \[ 9x + 36 - 3x < 2x. \] Combine like terms: \[ 6x + 36 < 2x. \] Now, isolate \( x \) by subtracting \( 2x \) from both sides: \[ 4x + 36 < 0. \] Then, subtract 36 from both sides: \[ 4x < -36. \] Finally, divide by 4: \[ x < -9. \] So the solution to the inequality is \( x < -9 \).