Solve for x: 0.72727x + 965.9089 = 0.85714x + 1014.57122.

Step-by-step solution

1. 1

   Move the $x$ terms to the side with the larger coefficient. Since $0.85714>0.72727$, subtracting $0.72727x$ from both sides keeps the remaining coefficient positive and avoids a sign flip later:

   $965.9089=(0.85714-0.72727)x+1014.57122=0.12987x+1014.57122$

2. 2

   Collect the constants. Subtract $1014.57122$ from both sides:

   $965.9089-1014.57122=-48.66232$

   so

   $-48.66232=0.12987x$

   The right-hand constant was the larger one, which is why the difference — and therefore $x$ — comes out negative.

3. 3

   Divide by the small coefficient and expect a large answer.

   $x=\frac{-48.66232}{0.12987}=-374.7002\ldots$

   Dividing by $0.12987$ multiplies the magnitude by nearly $8$. This sensitivity is the real lesson of the problem: an error of $0.01$ in the constant difference moves $x$ by about $0.08$, so keep full precision until the last step.

4. 4

   Round only at the end.

   $x\approx -374.70$

   Rounding the intermediate quotient to $-374.69$ (two decimals taken one step too early) is the mistake to avoid; the second decimal place is genuinely $0$, not $9$.

5. 5

   Check both sides at the solution. Left: $0.72727(-374.7002)+965.9089=693.4$ to one decimal. Right: $0.85714(-374.7002)+1014.57122=693.4$. The two sides agree, confirming $x\approx-374.70$.