Final answer:
The equation 'Nine times the difference of 5 and a number amounts to 63' translates to the algebraic expression 9(5 - x) = 63. Solving for 'x' yields x = -2. Therefore, the number that satisfies the equation is -2.
Step-by-step explanation:
To solve the equation: Nine times the difference of 5 and a number amounts to 63, we can set up an equation based on this statement. Let's let the unknown number be represented by ‘x’. The difference of 5 and a number is written as ‘(5 - x)’. Since the question states that nine times this difference equals 63, we can write the equation as 9(5 - x) = 63.
Now we solve for ‘x’:
- Multiply the difference by 9: 9 × 5 - 9 × x = 45 - 9x.
- Set the equation equal to 63: 45 - 9x = 63.
- Subtract 45 from both sides to isolate terms with ‘x’: -9x = 63 - 45.
- Simplify the right side: -9x = 18.
- Divide both sides by -9 to solve for ‘x’: x = 18/-9.
- Simplify to find the value of ‘x’: x = -2.
Therefore, the number we are looking for is -2, which matches answer choice D.