Solve for x: 0.58333x + 916.9998 = 0.72727x + 965.9089.

Step-by-step solution

1. 1

   Recognise the decimals for what they are. $0.58333\approx\tfrac{7}{12}$ and $0.72727\approx\tfrac{8}{11}$ are rounded fractions, so the data carry five-decimal precision at best. Work with the given decimals but do not claim more than about five significant figures in the answer.

2. 2

   Gather the $x$ terms on the larger-coefficient side. Subtract $0.58333x$ from both sides:

   $916.9998=(0.72727-0.58333)x+965.9089=0.14394x+965.9089$

3. 3

   Gather the constants.

   $916.9998-965.9089=-48.9091$

   giving

   $-48.9091=0.14394x$

4. 4

   Divide, keeping the intermediate digits.

   $x=\frac{-48.9091}{0.14394}=-339.78810\ldots\approx -339.79$

   Because $1/0.14394\approx 6.95$, the answer is roughly seven times the constant gap; truncating that quotient at $-339.78$ loses the correct rounding.

5. 5

   Verify by evaluating both sides. Left: $0.58333(-339.7881)+916.9998=718.80$. Right: $0.72727(-339.7881)+965.9089=718.80$. They match, so $x\approx-339.79$ is correct.