Let's simplify the given equation step by step:

(7x - 2.1) - (0.5 - 2x) = 0.9(3x - 1) + 0.1

First, simplify the expressions inside the parentheses:

7x - 2.1 - 0.5 + 2x = 2.7x - 0.9 + 0.1

Now, combine like terms on both sides of the equation:

9x - 2.6 = 2.7x - 0.8

Next, move all the x terms to one side of the equation and the constants to the other side:

9x - 2.7x = -0.8 + 2.6

6.3x = 1.8

Now, isolate x by dividing both sides by 6.3:

x = 1.8 / 6.3
x ≈ 0.2857

Therefore, the solution to the equation is x ≈ 0.2857.