Solve for x: 3,216.81 = x + 12.1 + (x times 0.019)/(1 - 0.019).

Step-by-step solution

1. 1

   Separate the constant from the x-terms. Only $12.1$ is free of $x$; move it to the left:

   $3216.81-12.1=x+\frac{0.019x}{0.981}\ \Longrightarrow\ 3204.71=x+\frac{0.019x}{0.981}.$

   Also simplify the denominator once and for all: $1-0.019=0.981$.

2. 2

   Factor x out of the right-hand side. This is the step that turns a fee equation into a one-line division:

   $3204.71=x\left(1+\frac{0.019}{0.981}\right).$

3. 3

   Evaluate the bracket — the gross-up multiplier.

   $\frac{0.019}{0.981}=0.01936799\ldots\ \Longrightarrow\ 1+0.01936799=1.01936799.$

   This number says that every dollar of net amount carries about $1.94$ cents of fee, slightly more than $1.9$ cents because the fee is charged on the gross rather than the net.

4. 4

   Divide to isolate x.

   $x=\frac{3204.71}{1.01936799}=3143.82051.$

5. 5

   Substitute back to check. The fee term is $\dfrac{0.019\times 3143.82051}{0.981}=60.88949$, so the right side totals

   $3143.82051+12.1+60.88949=3216.81,$

   matching the left side exactly. So x\approx\3{,}143.82$.