Solve for x: x - (0.8x - 5000)(0.03) = 6494.

Step-by-step solution

1. 1

   Read the structure. A quantity $x$ has a deduction taken from it, and the deduction is $3\%$ of an adjusted base $0.8x-5000$ rather than of $x$ itself. That nesting is the only thing that makes this harder than a one-step problem, and it is why the final coefficient will not be a round $0.97$.

2. 2

   Expand the product. Multiplying out the bracket:

   $0.03\,(0.8x-5000)=0.024x-150.$

   Check both pieces: $0.03\times0.8=0.024$ and $0.03\times5000=150$. Getting $0.024$ right — three decimal places, not two — is essential.

3. 3

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

   $x-\left(0.024x-150\right)=x-0.024x+150.$

   The $-150$ becomes $+150$; treating the deduction as a flat subtraction of $150$ instead is the most common error here.

4. 4

   Combine like terms and solve. Since $1-0.024=0.976$:

   $0.976x+150=6494\;\Longrightarrow\;0.976x=6344\;\Longrightarrow\;x=\frac{6344}{0.976}=6500.$

   The division comes out exactly: $0.976\times6500=6344$, so no rounding is involved and the answer is a clean whole number.

5. 5

   Substitute back into the original equation. The adjusted base is $0.8(6500)-5000=5200-5000=200$, the deduction is $0.03\times200=6$, and

   $6500-6=6494 ✓.$

   The deduction being just $6$ explains why $x$ ends up so close to the target value — worth noticing as a plausibility check before doing any arithmetic.