Solve for x: x - (0.8x - 5000)(0.1) = 7232.

Step-by-step solution

1. 1

   Expand the product. Multiplying the bracket by $0.1$:

   $0.1\,(0.8x-5000)=0.08x-500.$

   Both pieces shift one decimal place: $0.1\times0.8=0.08$ and $0.1\times5000=500$. A $10\%$ rate makes this arithmetic easy, but the structure is the same as for any rate.

2. 2

   Distribute the minus sign. The whole product is subtracted, so both of its terms change sign:

   $x-\left(0.08x-500\right)=x-0.08x+500.$

   The $-500$ becomes $+500$; missing that flip would shift the answer by more than a thousand.

3. 3

   Combine like terms. Since $1-0.08=0.92$, the equation is

   $0.92x+500=7232.$

   The coefficient $0.92$ is $1$ minus the effective rate $0.1\times0.8=0.08$ — the deduction bites on only $80\%$ of $x$, not all of it.

4. 4

   Isolate $x$ and keep the answer exact. Subtracting $500$ and dividing:

   $0.92x=6732\;\Longrightarrow\;x=\frac{6732}{0.92}=\frac{673200}{92}=\frac{168300}{23}\approx7317.39.$

   Since $23$ does not divide $168300$ the result is not a whole number — unlike the $3\%$ version of this problem, which lands exactly on $6500$.

5. 5

   Substitute back. The adjusted base is $0.8\times7317.3913-5000=5853.9130-5000=853.9130$, the deduction is $0.1\times853.9130=85.3913$, and

   $7317.3913-85.3913=7232.0000 ✓.$