Solve x - 0.2x = 6597.18 - 800 for x.

Step-by-step solution

1. 1

   Combine the like terms on the left. Treat $x$ as $1.0x$:

   $x-0.2x=(1-0.2)x=0.8x$

   This is exactly the arithmetic of taking $20\%$ off a price: what remains is $80\%$ of the original. Reading the equation this way makes the answer's size predictable — $x$ must be about $25\%$ larger than the right-hand side.

2. 2

   Simplify the right side.

   $6597.18-800=5797.18$

   so the equation is $0.8x=5797.18$.

3. 3

   Turn the division into an easier multiplication. Dividing by $0.8$ is the same as multiplying by $\frac{1}{0.8}=1.25$:

   $x=\frac{5797.18}{0.8}=1.25\times 5797.18$

4. 4

   Compute exactly. Multiplying by $1.25$ means adding a quarter of the number to itself:

   $5797.18+\frac{5797.18}{4}=5797.18+1449.295=7246.475$

   The result terminates at three decimals — no rounding is needed.

5. 5

   Check both readings. Directly: $0.8\times 7246.475=5797.18$ ✓. As a discount: $7246.475-0.2(7246.475)=7246.475-1449.295=5797.18$ ✓. So $x=7246.475$.