Solve 0.85x x 1.09 x 0.85 = 3250000/2.

Step-by-step solution

1. 1

   Simplify the right-hand side. $\dfrac{3{,}250{,}000}{2} = 1{,}625{,}000$, so the equation is $0.85x \cdot 1.09 \cdot 0.85 = 1{,}625{,}000$.

2. 2

   Collapse the multiplier chain on the left. All three decimals multiply $x$, so combine them into a single coefficient: $0.85 \cdot 1.09 = 0.9265, \qquad 0.9265 \cdot 0.85 = 0.787525.$ Reading the chain in business terms: two $15\%$ reductions and one $9\%$ increase leave $78.7525\%$ of the original.

3. 3

   Rewrite as a one-step linear equation. $0.787525x = 1{,}625{,}000.$ Only now is a single division enough to finish.

4. 4

   Divide, keeping full precision. $x = \frac{1{,}625{,}000}{0.787525} = \frac{65{,}000{,}000{,}000}{31{,}501} \approx 2{,}063{,}426.56.$ The exact value is the fraction $\tfrac{65000000000}{31501}$; rounding $0.787525$ to $0.7875$ first would shift the answer by about $65$, so do not truncate the coefficient.

5. 5

   Verify by running the chain forward. $2{,}063{,}426.5579 \times 0.85 = 1{,}753{,}912.574$, $\times 1.09 = 1{,}911{,}764.706$, $\times 0.85 = 1{,}625{,}000.00$ - the target is recovered.

6. 6

   Sanity-check the magnitude. Since the net multiplier $0.787525$ is less than $1$, $x$ must be larger than $1{,}625{,}000$; the ratio $1/0.787525 \approx 1.2698$ predicts about $2.06$ million, which matches.