Solve the given inequality. Write the solution set using interval notation. Graph the solution set.$\left|\frac{2-5x}{3}\right|\ge 5$

Key Concepts: Absolute Value Inequality, Interval Notation, Graphing Solution Set Explanation: To solve an absolute value inequality, we break the inequality into two separate inequalities - one where the algebraic expression inside the absolute value signs is positive and one where it is negative. We solve for x in both sets of inequalities, and then combine the solution sets. \n For the given inequality, we can write:$\frac{2-5x}{3}\le -5or\frac{2-5x}{3}\ge 5$ Rearrange to get: $-5x\le -17or-5x\ge 13$ Dividing both sides by -5, we get:$x\ge \frac{17}{5}orx\le -\frac{13}{5}$The solution set can be represented in interval notation as:$\left(-\infty ,-\frac{13}{5}\right]\cup \left[\frac{17}{5},\infty \right)$The graph of the solution set will be all real numbers except for the open interval $\left(-\frac{13}{5},\frac{17}{5}\right)$. Step by Step Solution: Step 1. Write the inequality as two separate inequalities. One with the algebraic expression inside the absolute value sign positive, and one with it negative. Step 2. Solve for x in both inequalities. Step 3. Combine the solution sets and represent the solution set using interval notation. Step 4. Plot the solution set on a number line to graph the solution set. Final Answer: { Solution set in interval notation: (-\infty, -\frac{13}{5}] \cup [\frac{17}{5}, \infty)\n Graph: https://imgur.com/xxxxxxxxx }