Solve for x: 122400000 + 0.72x + 2x + 1020000 + 400000 + 0.13(122400000 - 1200x) = 1200x.

Step-by-step solution

1. 1

   Combine the loose $x$-terms. Here the two unbracketed $x$-terms are $0.72x$ and $2x$:

   $0.72x+2x=2.72x$

   This is the only difference from the version with $12x$, and it changes nothing about the method — only the final coefficient.

2. 2

   Add the constants outside the bracket.

   $122400000+1020000+400000=123820000$

3. 3

   Expand the 13% bracket. Multiply through:

   $0.13\times 122400000=15912000,\qquad 0.13\times 1200x=156x$

   so the bracket becomes $15912000-156x$.

4. 4

   Collect once more. Constants: $123820000+15912000=139732000$. The $x$-terms:

   $2.72x-156x=-153.28x$

   so the equation reads $139732000-153.28x=1200x$.

5. 5

   Solve. Adding $153.28x$ to both sides gives

   $139732000=1353.28x\quad\Longrightarrow\quad x=\frac{139732000}{1353.28}=103254.3154\ldots$

6. 6

   Verify. Putting $x=103254.3154$ into the original expression gives $123905178.53$ on the left and $1200x=123905178.53$ on the right, so

   $x\approx 103254.32$