Solve x - (x*0.8 - 5000)*0.03 = 7226 for x.

Step-by-step solution

1. 1

   Expand the bracket before touching the subtraction. Multiplying each term inside by $0.03$:

   $0.03\left(0.8x-5000\right)=0.024x-150$

   Doing this first means you only have to worry about one sign change, in the next step.

2. 2

   Distribute the leading minus sign across both terms. This is where most sign errors happen: the minus applies to $-150$ as well, turning it into $+150$:

   $x-\left(0.024x-150\right)=x-0.024x+150$

   so the equation becomes

   $0.976x+150=7226$

3. 3

   Isolate the $x$-term. Subtract $150$ from both sides:

   $0.976x=7076$

4. 4

   Divide by the coefficient.

   $x=\frac{7076}{0.976}=\frac{7076000}{976}=7250$

   The division is exact here — $0.976\times 7250=7076$ with no rounding — which is a strong hint that $7226$ was chosen deliberately.

5. 5

   Check in the original equation. With $x=7250$: $0.8(7250)=5800$, so $5800-5000=800$, and $0.03\times 800=24$. Then $7250-24=7226\ \checkmark$. Notice the check runs through the original bracket, not the expanded form, so it would also catch a distribution mistake.