Question

1. |10 + 4n| < 46

Explanation:

Step1: Apply absolute value inequality rule

For \(|x| < a\) (where \(a>0\)), we have \(-a < x < a\). So for \(|10 + 4n| < 46\), we get \(-46 < 10 + 4n < 46\).

Step2: Subtract 10 from all parts

Subtract 10 from each part of the compound inequality: \(-46 - 10 < 10 + 4n - 10 < 46 - 10\), which simplifies to \(-56 < 4n < 36\).

Step3: Divide by 4

Divide each part by 4: \(\frac{-56}{4} < \frac{4n}{4} < \frac{36}{4}\), so \(-14 < n < 9\).

Answer:

The solution to the inequality \(|10 + 4n| < 46\) is \(-14 < n < 9\).