Which equation models the problem and shows the correct solution?

The difference between [tex]\( x \)[/tex] and 89 is 7.

A. Write the equation as [tex]\( 89 - x = 7 \)[/tex] and subtract 7 from both sides. The answer is 82.

B. Write the equation as [tex]\( x - 89 = 7 \)[/tex] and add 89 to both sides. The answer is 96.

C. Write the equation as [tex]\( x - 7 = 89 \)[/tex] and add 7 to both sides. The answer is 96.

D. Write the equation as [tex]\( 7 - x = 89 \)[/tex] and subtract 7 from both sides. The answer is 82.

To solve the problem, we need to translate the statement "The difference between [tex]\( x \)[/tex] and 89 is 7" into a mathematical equation and then solve it.

1. Understand the Problem Statement:
- "The difference between [tex]\( x \)[/tex] and 89 is 7" means that if you subtract 89 from [tex]\( x \)[/tex], the result is 7.

2. Write the Equation:
- The equation that fits the problem statement is [tex]\( x - 89 = 7 \)[/tex].

3. Solve the Equation:
- We need to solve for [tex]\( x \)[/tex]. To do this, add 89 to both sides of the equation:
[tex]\[
x - 89 + 89 = 7 + 89
\][/tex]
[tex]\[
x = 96
\][/tex]

4. Verify the Solution:
- Ensure that the solution makes sense by substituting [tex]\( x \)[/tex] back into the problem statement:
[tex]\[
\text{The difference between } 96 \text{ and } 89 \text{ is } 7.
\][/tex]
[tex]\[
96 - 89 = 7
\][/tex]

Therefore, the correct equation is [tex]\( x - 89 = 7 \)[/tex]. Adding 89 to both sides gives us the correct solution, [tex]\( x = 96 \)[/tex].

So, the correct choice is:
- Write the equation as [tex]\( x - 89 = 7 \)[/tex] and add 89 to both sides. The answer is 96.