Solve and write interval notation for the solution set. Then graph the solution set. \[ |6-4 x| \geq 16 \] Select the correct choice below and, if necessary, fill in the answer box to complete A. The solution cot ic

To solve the inequality \( |6-4x| \geq 16 \), we start by breaking it into two cases: 1. \( 6 - 4x \geq 16 \) 2. \( 6 - 4x \leq -16 \) **For the first case**: - Subtract 6 from both sides: \(-4x \geq 10\) - Divide by -4 (remember to flip the inequality sign): \(x \leq -\frac{5}{2}\) **For the second case**: - Subtract 6 from both sides: \(-4x \leq -22\) - Divide by -4 (flip the inequality sign): \(x \geq \frac{11}{2}\) Thus, the solution set in interval notation is: \[ (-\infty, -\frac{5}{2}] \cup [\frac{11}{2}, \infty) \] To graph the solution set, you would plot a number line with closed circles on \(-\frac{5}{2}\) and \(\frac{11}{2}\) and shade to the left from \(-\frac{5}{2}\) and to the right from \(\frac{11}{2}\).