Solve for x: 16000000 * (0.11 + 0.0006) + 0.13 * x = x.

Step-by-step solution

1. 1

   Simplify the bracket before multiplying. Adding the two rates:

   $0.11+0.0006=0.1106$

   Line the decimals up carefully — $0.11$ is $0.1100$, so the sum is $0.1106$, not $0.116$.

2. 2

   Evaluate the constant product.

   $16000000\times 0.1106=1769600$

   A quick check: $16\,000\,000\times 0.11=1\,760\,000$ and $16\,000\,000\times 0.0006=9\,600$, and $1760000+9600=1769600$ ✓. The equation is now $1769600+0.13x=x$.

3. 3

   Remember the bare $x$ has coefficient 1. Subtracting $0.13x$ from both sides:

   $1769600=x-0.13x=(1-0.13)x=0.87x$

   Treating the lone $x$ as if it had no coefficient — and writing $1769600=0.13x$ or $1769600=-0.87x$ — is the standard mistake in equations of this shape.

4. 4

   Divide by 0.87.

   $x=\frac{1769600}{0.87}=\frac{176960000}{87}=2034022.9885\ldots\approx 2034022.99$

   Converting to the exact fraction first keeps every digit honest before rounding to cents.

5. 5

   Verify by substitution. Left side: $1769600+0.13\times 2034022.99=1769600+264422.99=2034022.99$, which equals the right side ✓. Notice the answer is larger than the constant $1769600$ by exactly the $13\%$ that was added back, which is the sanity check to expect.