x - [3x - 2(9 - x)] - 1 < x - (5 - x)

Multiply the - 2 by the 9 and write - 18
Multiply the - 2 by the - x and write + 2x

x - [3x - 18 + 2x] - 1 < x - (5 - x)

Combine the 3x and the + 2x and write 5x

x - [5x - 18] - 1 < x - (5 - x)

Put a 1 just before the bracket on the left 
and a 1 just before the parentheses on the 
right:

x - 1[5x - 18] - 1 < x - 1(5 - x)

Multiply the - 1 by the 5x and write - 5x
Multiply the - 1 by the - 18 and write + 18
Multiply the - 1 by the 5 and write - 5
Multiply the - 1 by the - x and write + x

x - 5x + 18 - 1 < x - 5 + x

Combine the x and the - 5x and write -4x
Combine the + 18 and the - 1 and write + 17
On the right, combine the x and the + x and write 2x

       -4x + 17 < 2x - 5

Add -17 to both sides

            -4x < 2x - 22

Add -2x to both sides:

            -6x < -22

Divide both sides by -6, remembering that when
you divide an inequality by a negative number,
the inequality is reversed:

            > 

               x >     

Edwin