Solve 4x - 0.35(x - 1) = 245.85 for x.

Step-by-step solution

1. 1

   Expand the bracket and watch the double negative.

   $4x-0.35(x-1)=4x-0.35x+0.35$

   The $-1$ inside the bracket meets the $-0.35$ outside and produces $+0.35$.

2. 2

   Collect the $x$ terms. $4x-0.35x=3.65x$, so the equation is

   $3.65x+0.35=245.85$

   A useful check on this coefficient: $4-0.35$ must be $3.65$, and the constant that appeared is exactly $0.35$ — the same number, which is a signature of the $(x-1)$ shift.

3. 3

   Subtract the constant.

   $3.65x=245.85-0.35=245.50$

   The right-hand side lands on a clean two-decimal value, which is a hint the source problem was designed around it.

4. 4

   Divide and reduce to lowest terms. Scale by $100$ and cancel the factor $5$:

   $x=\frac{245.50}{3.65}=\frac{24550}{365}=\frac{4910}{73}$

   $73$ is prime and $4910=73\cdot 67+19$, so no further cancellation is possible.

5. 5

   Get the decimal and verify. $x=67+\frac{19}{73}=67.260274\ldots$ Then $3.65\cdot 67.260274=245.50$ and $245.50+0.35=245.85$, matching the original right-hand side exactly.