Solve the following inequality and give the solution in interval notation. \( -4 x+1<4[(x+3)-2 x]-1 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set in the interval notation is B. Tfre solution set is the empty set.

To solve the inequality \( -4x+1<4[(x+3)-2x]-1 \), let's simplify the right side first. 1. Distribute the 4: \[ 4[(x+3)-2x] = 4[x+3-2x] = 4[-x+3] = -4x + 12 \] Substituting this into the inequality gives: \[ -4x + 1 < -4x + 12 - 1 \] which simplifies to: \[ -4x + 1 < -4x + 11 \] 2. Adding \(4x\) to both sides, we have: \[ 1 < 11 \] This is always true. Therefore, \(x\) can take any real number, and the solution set is all real numbers. The solution set in the interval notation is: \[ \text{A. The solution set in interval notation is } (-\infty, \infty). \]