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------------------------------------------------ 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 and find which equation correctly models the situation, let's break down the problem step-by-step.

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

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

2. Writing the Equation:
- Based on this understanding, the equation can be written as:
[tex]\[
x - 89 = 7
\][/tex]

3. Solving the Equation:
- To solve for [tex]\(x\)[/tex], you need to isolate [tex]\(x\)[/tex] on one side of the equation.
- Add 89 to both sides of the equation:
[tex]\[
x - 89 + 89 = 7 + 89
\][/tex]
- This simplifies to:
[tex]\[
x = 96
\][/tex]

4. Verifying the Option:
- The option that matches the equation we formed and solved is: "Write the equation as [tex]\(x - 89 = 7\)[/tex] and add 89 to both sides. The answer is 96."

Thus, the correct equation to model the problem is [tex]\(x - 89 = 7\)[/tex], and the solution is [tex]\(x = 96\)[/tex].