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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.

Answer :

We start with the statement:

[tex]$$
\text{"The difference between } x \text{ and } 89 \text{ is } 7.
$$[/tex]

One way to interpret "the difference between [tex]$x$[/tex] and [tex]$89$[/tex]" is to assume that [tex]$x$[/tex] is greater than [tex]$89$[/tex]. In this case, the statement can be modeled by the equation

[tex]$$
x - 89 = 7.
$$[/tex]

To solve for [tex]$x$[/tex], follow these steps:

1. Set up the equation:

[tex]$$
x - 89 = 7.
$$[/tex]

2. Add 89 to both sides:

[tex]$$
x - 89 + 89 = 7 + 89.
$$[/tex]

3. Simplify the equation:

[tex]$$
x = 96.
$$[/tex]

Thus, the equation that correctly models the problem is

[tex]$$
x - 89 = 7,
$$[/tex]

and the solution is [tex]$x = 96$[/tex].

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