Solve for x: x - ((36000 + x) - 35000) * 0.03 - 180 = 6500.

Step-by-step solution

1. 1

   Collapse the nested brackets first. The inner expression contains only constants and one $x$:

   $(36000+x)-35000=x+1000$

   so the equation becomes

   $x-0.03(x+1000)-180=6500$

   Doing this before distributing keeps the $0.03$ from being multiplied across three terms instead of two.

2. 2

   Distribute the $-0.03$ across both terms.

   $x-0.03x-30-180=6500$

   Note $0.03\times 1000=30$, and it is subtracted because the whole bracket is subtracted.

3. 3

   Combine like terms on the left. The $x$ terms give $1-0.03=0.97$, and the constants give $-30-180=-210$:

   $0.97x-210=6500$

   The coefficient $0.97$ is the readable meaning of the problem: $3\%$ of the excess is taken away, so $97\%$ of $x$ survives.

4. 4

   Isolate the $x$ term. Add $210$ to both sides:

   $0.97x=6710$

5. 5

   Divide by $0.97$ carefully.

   $x=\frac{6710}{0.97}=\frac{671000}{97}=6917.5258\ldots\approx 6917.53$

   Converting to the exact fraction $\tfrac{671000}{97}$ before dividing is the safest way to get the digits right; the nearby wrong value $6918.56$ comes from a single mis-carried digit in the long division.

6. 6

   Check by substituting back. With $x=6917.5258$: the bracket is $7917.5258$, times $0.03$ is $237.5258$, so the left side is $6917.5258-237.5258-180=6500.0000$ ✓. (Using $6918.5567$ instead would give $6501.00$, one whole unit off.)