Solve 0.8 times the quantity 1 plus x over 10000 equals 5.

Step-by-step solution

1. 1

   Peel the operations off from the outside in. Reading the left side outward, $x$ is divided by $10000$, then $1$ is added, then the whole bracket is multiplied by $0.8$. To isolate $x$ we undo that list in reverse order: divide by $0.8$, subtract $1$, multiply by $10000$. Expanding the bracket also works but creates the awkward coefficient $0.00008$.

2. 2

   Undo the multiplication by 0.8.

   $1+\frac{x}{10000}=\frac{5}{0.8}=\frac{50}{8}=6.25$

   Writing $5/0.8$ as $50/8$ first makes it obvious the quotient is exactly $6.25$, not a rounded decimal.

3. 3

   Undo the addition of 1.

   $\frac{x}{10000}=6.25-1=5.25$

4. 4

   Undo the division by 10000.

   $x=5.25\times 10000=52500$

   Multiplying a decimal by $10^4$ just shifts the point four places.

5. 5

   Substitute back. $\dfrac{52500}{10000}=5.25$, so $1+5.25=6.25$ and $0.8\cdot 6.25=5$. The equation is satisfied exactly, with no rounding, so $x=52500$.