Solve the absolute value inequality. \[ |4(x-1)+10| \leq 26 \]

Step 1 ：First, we remove the absolute value from the inequality |4(x-1)+10| ≤ 26. This gives us two inequalities: 4(x-1)+10 ≤ 26 and -(4(x-1)+10) ≤ 26.

Step 2 ：Solving the first inequality, 4(x-1)+10 ≤ 26, we find that x ≤ 5.

Step 3 ：Solving the second inequality, -(4(x-1)+10) ≤ 26, we find that x ≥ -8.

Step 4 ：The solution to the original inequality is the intersection of the solutions to these two inequalities. Therefore, the solution is -8 ≤ x ≤ 5.