Compute x = 0.6 x 963 - 402.8.

Step-by-step solution

1. 1

   Apply the order of operations. Multiplication outranks subtraction, so the product $0.6\times963$ must be evaluated before anything is taken away. Subtracting first — $963-402.8$, then scaling — would give a completely different (wrong) answer.

2. 2

   Multiply 0.6 by 963. Treat it as $\tfrac{6}{10}\times963$: since $6\times963=5778$, dividing by $10$ gives

   $0.6\times963=577.8$

   One decimal place in, one decimal place out.

3. 3

   Estimate the result before subtracting. $577.8-402.8$ is roughly $578-403=175$, so the answer should be right about $175$.

4. 4

   Subtract 402.8. Both numbers share the same tenths digit, $8$, so the decimals cancel exactly:

   $577.8-402.8=175$

   The answer is a whole number — a useful signal that the arithmetic is clean rather than rounded.

5. 5

   Verify by reversing the operations. Adding back: $175+402.8=577.8$ ✓, and dividing by $0.6$: $577.8/0.6=963$ ✓. Both checks return the original inputs, confirming $x=175$.