To solve this inequality, we first need to simplify both sides of the equation.

5(x-4) + x ≥ 2(x-2) + x + 3
5x - 20 + x ≥ 2x - 4 + x + 3
6x - 20 ≥ 3x - 1

Now, we want to isolate x on one side of the inequality. We can do this by subtracting 3x from both sides.

6x - 3x - 20 ≥ -1
3x - 20 ≥ -1

Next, we add 20 to both sides to get x by itself:

3x - 20 + 20 ≥ -1 + 20
3x ≥ 19

Finally, we divide by 3 to solve for x:

3x/3 ≥ 19/3
x ≥ 19/3 or x ≥ 6.33

Therefore, the solution to the inequality is x ≥ 6.33.