Solve the given inequality. Write the solution set using interval notation, then graph it. \( \frac{5-4 \mathrm{x}}{3} \geq-4 \)

To solve the inequality \( \frac{5-4x}{3} \geq -4 \), we start by multiplying both sides by 3 to eliminate the fraction: \[ 5 - 4x \geq -12. \] Next, we isolate \( x \) by subtracting 5 from both sides: \[ -4x \geq -17. \] Now, divide both sides by -4, and remember to flip the inequality sign: \[ x \leq \frac{17}{4}. \] In interval notation, the solution set is: \[ (-\infty, \frac{17}{4}]. \] To graph this solution, you would draw a number line, shading everything to the left of \( \frac{17}{4} \) which is \( 4.25 \) and placing a closed dot at \( \frac{17}{4} \) to indicate that this point is included in the solution. Happy graphing!