Question

write an inequality: twenty-two more than four times a number is less than 82. 82 + 22n ≥ 4; 22 + 4n ≤ 82; 22 + 4n > 82; 22 + 4n < 82

Explanation:

Step1: Define the variable

Let the number be \( n \).

Step2: Translate "four times a number"

Four times a number \( n \) is \( 4n \).

Step3: Translate "twenty - two more than four times a number"

Twenty - two more than \( 4n \) means we add 22 to \( 4n \), so it is \( 22 + 4n \).

Step4: Translate "is less than 82"

The phrase "is less than" corresponds to the inequality symbol \( < \), and the number we are comparing to is 82. So the inequality is \( 22+4n < 82 \).

Answer:

\( 22 + 4n < 82 \) (the option corresponding to this inequality in the given choices)