Solve the following inequality and graph the solution set. \( |-4 x+2| \leq 1 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any nut B. The solution set is \( \varnothing \).

We are given the inequality   |–4x + 2| ≤ 1. Step 1. Rewrite the inequality as a double inequality:   –1 ≤ –4x + 2 ≤ 1. Step 2. Solve the left part:   –1 ≤ –4x + 2   Subtract 2 from both sides:   –1 – 2 ≤ –4x   –3 ≤ –4x   Now, divide by –4 (remembering to reverse the inequality sign when dividing by a negative number):   (–3)/(–4) ≥ x  or  x ≤ 3/4. Step 3. Solve the right part:   –4x + 2 ≤ 1   Subtract 2 from both sides:   –4x ≤ 1 – 2   –4x ≤ –1   Divide by –4 (again, reversing the inequality):   x ≥ (–1)/(–4)  or  x ≥ 1/4. Step 4. Combine the two results:   x must satisfy both conditions:   x ≥ 1/4 and x ≤ 3/4. Thus, the solution set is:   [1/4, 3/4]. Graphing the solution on a number line:   • Place closed circles (•) at x = 1/4 and x = 3/4 to indicate that these endpoints are included.   • Shade the region between these circles to show all the numbers between 1/4 and 3/4 are part of the solution set. Answer Choice:   A. The solution set is [1/4, 3/4].