College

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 by translating the phrase “The difference between [tex]\( x \)[/tex] and 89 is 7” into an algebraic equation. This can be written as

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

Next, we solve for [tex]\( x \)[/tex] by isolating it on one side of the equation. To do so, add 89 to both sides:

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

which simplifies to

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

Finally, adding the numbers gives

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

Thus, the correct model of the problem is

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

and the solution is [tex]\( x = 96 \)[/tex].

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