Solve 286.2 + 3.3x = 316 + 2x for x.

Step-by-step solution

1. 1

   Move the $x$ terms to the side with the larger coefficient. Subtracting $2x$ from both sides keeps the coefficient positive:

   $286.2+1.3x=316$

   The working coefficient $1.3=3.3-2$ is small compared with the constants, which is why the answer is much larger than the gap between them.

2. 2

   Move the constants to the other side.

   $1.3x=316-286.2=29.8$

3. 3

   Divide, and clear the decimals to get the exact value.

   $x=\frac{29.8}{1.3}=\frac{298}{13}$

   Both parts were multiplied by $10$. Since $13$ is prime and does not divide $298$ ($13\cdot 22=286$, remainder $12$), the answer is not a terminating decimal.

4. 4

   Write the decimal expansion.

   $x=22+\frac{12}{13}=22.923076923\ldots\approx 22.9231$

   The repeating block $923076$ comes from the twelfth of a thirteenth.

5. 5

   Check both sides. Left: $286.2+3.3(22.9230769)=286.2+75.6461538=361.8461538$. Right: $316+2(22.9230769)=316+45.8461538=361.8461538$. They agree, so $x=\frac{298}{13}$.