To solve the equation (-5|5x - 2| - 3 = -18), we can follow these steps:1. First, add 3 to both sides of the equation to isolate the absolute value term:[ -5|5x - 2| = -18 + 3 ][ -5|5x - 2| = -15 ]2. Next, divide both sides by -5 to get rid of the coefficient in front of the absolute value term:[ |5x - 2| = frac{-15}{-5} ][ |5x - 2| = 3 ]3. Now, we split the equation into two cases:Case 1: (5x - 2) is positive:[ 5x - 2 = 3 ]Case 2: (5x - 2) is negative:[ -(5x - 2) = 3 ]4. Solve each case separately:For Case 1:[ 5x - 2 = 3 ][ 5x = 3 + 2 ][ 5x = 5 ][ x = frac{5}{5} ][ x = 1 ]For Case 2:[ -(5x - 2) = 3 ][ -5x + 2 = 3 ][ -5x = 3 - 2 ][ -5x = 1 ][ x = frac{1}{-5} ][ x = -frac{1}{5} ]So, the solutions to the equation are (x = 1) and (x = -frac{1}{5}).