Question

1. \\(\frac{n}{8} - 7 > -8\\)

(number line from -10 to 0 with ticks at -10, -8, -6, -4, -2, 0)

Explanation:

Step1: Add 7 to both sides

To isolate the term with \( n \), we add 7 to both sides of the inequality \(\frac{n}{8}-7 > -8\). This gives us \(\frac{n}{8}-7 + 7> -8 + 7\), which simplifies to \(\frac{n}{8}>-1\).

Step2: Multiply both sides by 8

To solve for \( n \), we multiply both sides of the inequality \(\frac{n}{8}>-1\) by 8. This gives us \(\frac{n}{8}\times8>-1\times8\), which simplifies to \(n > - 8\).

Answer:

The solution to the inequality \(\frac{n}{8}-7 > -8\) is \(n > -8\). On the number line, this would be represented by an open circle at \(-8\) (since \(n\) is not equal to \(-8\)) and an arrow pointing to the right (towards positive infinity).