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Write an inequality: Twenty-two more than four times a number is less than 82.

A. [tex]22 + 4n \geq 82[/tex]
B. [tex]22 + 4n \textgreater 82[/tex]
C. [tex]22 + 4n \textless 82[/tex]
D. [tex]22 + 4n \leq 82[/tex]

Answer :

We begin by translating the phrase into an inequality. "Four times a number" means [tex]$4n$[/tex], and "twenty-two more than four times a number" is written as [tex]$22 + 4n$[/tex]. The phrase "is less than 82" tells us to set up the inequality:

[tex]$$
22 + 4n < 82.
$$[/tex]

Now, we solve the inequality step by step:

1. Subtract 22 from both sides:
We subtract 22 from both sides to isolate the term with [tex]$n$[/tex]:

[tex]$$
22 + 4n - 22 < 82 - 22,
$$[/tex]

which simplifies to

[tex]$$
4n < 60.
$$[/tex]

2. Divide both sides by 4:
Dividing both sides by 4 gives:

[tex]$$
n < \frac{60}{4},
$$[/tex]

so

[tex]$$
n < 15.
$$[/tex]

Thus, the inequality that corresponds to the statement is:

[tex]$$
22 + 4n < 82.
$$[/tex]

This is the correct answer.

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