(a) Solve the inequality \( 1+\frac{x-5}{3}-2 x<-4 \)

To solve the inequality \( 1+\frac{x-5}{3}-2x<-4 \), let's first simplify it step by step. Start by isolating the fraction: \[ \frac{x-5}{3} - 2x < -4 - 1 \] \[ \frac{x-5}{3} - 2x < -5 \] Now, multiply the entire inequality by 3 to eliminate the fraction (remember that multiplying by a positive number doesn’t change the direction of the inequality): \[ x - 5 - 6x < -15 \] Combine like terms: \[ -x - 5 < -15 \] Now, add 5 to both sides: \[ -x < -10 \] Finally, multiply by -1 (which reverses the inequality): \[ x > 10 \] Thus, the solution to the inequality is: \[ \boxed{x > 10} \]