g) \( 4 x-\frac{2 x-1}{3}+1<0 \)

To solve the inequality \( 4x - \frac{2x - 1}{3} + 1 < 0 \), first simplify the expression. Combine like terms and eliminate the fraction by multiplying through by 3 (not changing the direction of the inequality since 3 is positive): \[ 3(4x) - (2x - 1) + 3 < 0 \] This simplifies to: \[ 12x - 2x + 1 + 3 < 0 \] Combining those gives you: \[ 10x + 4 < 0 \] Now isolate \( x \): \[ 10x < -4 \] Dividing both sides by 10 results in: \[ x < -\frac{2}{5} \] So, the solution for the inequality is \( x < -\frac{2}{5} \).