Solve for x: 1077.38 = 0.35x + 0.35 * 1077.38.

Step-by-step solution

1. 1

   Evaluate the numeric product first. The term $0.35\times1077.38$ contains no unknown, so compute it before rearranging:

   $0.35\times1077.38=377.083.$

   Checking by parts: $0.35\times1000=350$ and $0.35\times77.38=27.083$, summing to $377.083$ ✓.

2. 2

   Rewrite as a two-step linear equation. The equation becomes

   $1077.38=0.35x+377.083,$

   which is now the familiar $c=ax+b$ shape with $a=0.35$ and $b=377.083$.

3. 3

   Undo the addition. Subtracting $377.083$ from both sides:

   $1077.38-377.083=0.35x\;\Longrightarrow\;700.297=0.35x.$

   Line up decimal points: $1077.380-377.083=700.297$.

4. 4

   Undo the multiplication. Dividing both sides by $0.35$:

   $x=\frac{700.297}{0.35}=2000.848571\ldots\approx 2000.85.$

   Dividing by $0.35$ is the same as multiplying by $\tfrac{100}{35}=\tfrac{20}{7}$, so an exact form is $x=\tfrac{20}{7}\times700.297$.

5. 5

   Notice the shortcut and use it as a check. Because the same constant $1077.38$ appears on both sides, factoring gives

   $1077.38\,(1-0.35)=0.35x\;\Longrightarrow\;x=1077.38\times\frac{0.65}{0.35}=2000.8486,$

   matching the step-by-step answer ✓. Substituting back: $0.35(2000.8486)+377.083=700.297+377.083=1077.380$ ✓.