Use the inequality to answer Parts 1-3. \( -3(x-2) \leq \frac{1}{3} \) Part i: Solve the inequality. Leave answer In terms of a whole number or reduced improper fraction. Part 2: Write a verbal statement describing the solution to the inequality. Part 3: Verify your solution to the inequality using two elements of the solution set.

To solve the inequality \( -3(x-2) \leq \frac{1}{3} \), first distribute the -3: \[ -3x + 6 \leq \frac{1}{3} \] Next, subtract 6 from both sides: \[ -3x \leq \frac{1}{3} - 6 \] Convert 6 to a fraction: \[ -3x \leq \frac{1}{3} - \frac{18}{3} = \frac{-17}{3} \] Now, divide both sides by -3, remembering to flip the inequality: \[ x \geq \frac{17}{9} \] --- The solution to the inequality means that any value of \( x \) that is greater than or equal to \( \frac{17}{9} \) satisfies the condition. This can be understood as "x can take on values starting from \( \frac{17}{9} \) and extending infinitely larger." --- To verify the solution, we can choose two numbers from the solution set. First, let's try \( x = 2 \): \[ -3(2-2) \leq \frac{1}{3} \rightarrow 0 \leq \frac{1}{3} \quad \text{(True)} \] Now let's test \( x = 3 \): \[ -3(3-2) \leq \frac{1}{3} \rightarrow -3 \leq \frac{1}{3} \quad \text{(True)} \] Since both numbers work, our solution \( x \geq \frac{17}{9} \) is verified!