Solve for x: x - 2400000x/8844796 = 1200000. Give the exact value and a decimal.

Step-by-step solution

1. 1

   Factor $x$ out of the left-hand side. Both terms contain $x$, so

   $x\left(1-\frac{2400000}{8844796}\right)=1200000.$

   This is much safer than multiplying the whole equation by $8844796$ first: it keeps the large number in one place instead of spreading it across every term.

2. 2

   Combine the bracket into a single fraction. Writing $1=\frac{8844796}{8844796}$:

   $1-\frac{2400000}{8844796}=\frac{8844796-2400000}{8844796}=\frac{6444796}{8844796}.$

   The subtraction $8844796-2400000=6444796$ is the one piece of arithmetic worth double-checking, since every later digit depends on it.

3. 3

   Solve by multiplying by the reciprocal. From $x\cdot\frac{6444796}{8844796}=1200000$:

   $x=1200000\cdot\frac{8844796}{6444796}=\frac{10613755200000}{6444796}.$

   Dividing numerator and denominator by $4$ gives the reduced exact value

   $x=\frac{2653438800000}{1611199}.$

4. 4

   Convert to a decimal carefully. Carrying out the division,

   $x=1646872.1740765\ldots\approx 1{,}646{,}872.17.$

   A rounded intermediate — for instance replacing $\frac{6444796}{8844796}$ by $0.7287$ — shifts the answer by well over a hundred, so the fraction should be carried all the way to the final division.

5. 5

   Substitute back to confirm. With $x=\frac{2653438800000}{1611199}$,

   $x-\frac{2400000x}{8844796}=x\cdot\frac{6444796}{8844796}=1200000.000000 ✓.$

   A quick plausibility check also works: the coefficient of $x$ is about $0.7287$, and $\frac{1200000}{0.7287}\approx 1{,}646{,}768$ — the right size, but only the first four significant figures agree, which is exactly the hundred-plus shift warned about above.