Solve x - (x*0.8 - 5000)*0.03 = 7232 for x, giving an exact answer.

Step-by-step solution

1. 1

   Expand the bracket. Distributing $0.03$ over the two inner terms:

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

2. 2

   Subtract the whole bracket, flipping both signs.

   $x-\left(0.024x-150\right)=x-0.024x+150=0.976x+150$

   so the equation reads

   $0.976x+150=7232$

3. 3

   Isolate and divide. Subtracting $150$ gives $0.976x=7082$, hence

   $x=\frac{7082}{0.976}$

4. 4

   Convert to an exact fraction rather than rounding. Multiply numerator and denominator by $1000$ and cancel:

   $x=\frac{7082000}{976}=\frac{442625}{61}$

   since $\gcd(7082000,976)=16$. Because $61$ is prime and does not divide $10$, this fraction has a non-terminating decimal expansion, $x=7256.1475409836\ldots$ — unlike the neighbouring problem with $7226$ on the right, which lands exactly on $7250$.

5. 5

   Decide how to report it. Give $\dfrac{442625}{61}$ when an exact answer is wanted, or $x\approx 7256.15$ to two decimal places for a money-style context.

6. 6

   Check. $0.976\times\dfrac{442625}{61}=7082$ exactly, and $7082+150=7232\ \checkmark$; numerically $7256.147540983607-0.03\left(0.8\cdot 7256.147540983607-5000\right)=7232.000000$.