Solve for x: x = (500000 - 100000 - 50000 - x) x 12%.

Step-by-step solution

1. 1

   Convert the percentage to a decimal. A percentage is a fraction with denominator $100$, so

   $12\%=\frac{12}{100}=0.12,$

   and the equation becomes

   $x=(500000-100000-50000-x)\times 0.12.$

   Leaving the $\%$ sign in place while doing algebra is the fastest way to lose a factor of $100$.

2. 2

   Simplify the known part of the bracket. The three constants combine independently of $x$:

   $500000-100000-50000=350000,$

   so

   $x=0.12\,(350000-x).$

   Notice that $x$ appears on both sides — this is a self-referential equation (the kind that shows up when a fee is a percentage of what is left after the fee), not a one-step arithmetic problem.

3. 3

   Expand the right-hand side. Distributing the $0.12$ over both terms:

   $x=0.12\times 350000-0.12x=42000-0.12x.$

   Check the product: $350000\times 0.12=350000\times\tfrac{12}{100}=3500\times 12=42000$ ✓.

4. 4

   Collect the $x$ terms and divide. Adding $0.12x$ to both sides gathers the unknown on the left:

   $x+0.12x=42000\;\Longrightarrow\;1.12x=42000\;\Longrightarrow\;x=\frac{42000}{1.12}=37500.$

   The coefficient $1.12$ — not $0.88$ — is what makes this different from "12% of 350000"; the answer $37500$ is genuinely smaller than $42000$.

5. 5

   Substitute back into the original statement. The bracket becomes $350000-37500=312500$, and

   $312500\times 0.12=37500 ✓.$

   The consistency check is worth doing precisely because self-referential equations are easy to set up backwards.