Solve for x: 364.4210x + 364.4210 = 215900.9.

Step-by-step solution

1. 1

   Standard route: undo the addition first. Subtracting $364.4210$ from both sides isolates the $x$ term:

   $364.4210x=215900.9-364.4210=215536.479.$

   Line up the decimal points when subtracting: $215900.900-364.421=215536.479$, with the trailing zeros written in to keep the columns honest.

2. 2

   Divide by the coefficient. Dividing both sides by $364.4210$:

   $x=\frac{215536.479}{364.4210}=591.449117916\ldots\approx 591.4491.$

   Dividing by a decimal is the same as multiplying numerator and denominator by $10^{4}$, i.e. $\frac{2155364790}{3644210}$, if you prefer to work with whole numbers.

3. 3

   Faster route: notice the repeated coefficient. The number $364.4210$ multiplies $x$ and stands alone, so factor it out:

   $364.4210\,(x+1)=215900.9\;\Longrightarrow\;x+1=\frac{215900.9}{364.4210}=592.449117916.$

   Subtracting $1$ gives $x=591.449117916$ — the same value with only one division instead of a subtraction plus a division.

4. 4

   Reconcile the two routes. They must agree, because $\frac{a\,b-a}{a}=b-1$ is an identity; here $\frac{215900.9}{364.4210}$ and $\frac{215536.479}{364.4210}$ differ by exactly $\frac{364.4210}{364.4210}=1$ ✓. Spotting the shared coefficient also gives a fast estimate: $215900.9/364\approx 593$, so the answer must be near $592$.

5. 5

   Check by substitution. With $x=591.449117916$,

   $364.4210\times 591.449117916=215536.479,\qquad 215536.479+364.4210=215900.900 ✓.$

   Rounding $x$ to $591.45$ before substituting would return $215901.22$ instead — close, but a reminder to round only at the very end.