Solve the given inequality. Write the solution set using interval notation, then graph it. \( \frac{5-5 x}{3} \geq-2 \)

To solve the inequality: \[ \frac{5 - 5x}{3} \geq -2 \] **Step 1: Eliminate the Fraction** Multiply both sides of the inequality by 3 (since 3 is positive, the direction of the inequality remains unchanged): \[ 5 - 5x \geq -6 \] **Step 2: Isolate the Variable Term** Subtract 5 from both sides: \[ -5x \geq -11 \] **Step 3: Solve for \( x \)** Divide both sides by -5. **Remember**: Dividing by a negative number reverses the inequality sign. \[ x \leq \frac{11}{5} \] \[ x \leq 2.2 \] **Solution Set in Interval Notation:** \[ (-\infty, \ 2.2] \] **Graph of the Solution:** Below is a number line representing the solution \( x \leq 2.2 \). ``` <========●================> 2.2 ``` - The closed circle (●) at 2.2 indicates that 2.2 is included in the solution. - The arrow pointing to the left (towards \(-\infty\)) shows that all numbers less than or equal to 2.2 are part of the solution.