Question

1. $-18n > -144$

Explanation:

Step1: Divide both sides by -18 (reverse inequality)

To solve the inequality \(-18n > -144\), we divide both sides by \(-18\). Remember that when dividing or multiplying both sides of an inequality by a negative number, the direction of the inequality sign reverses. So we have:
\[
\frac{-18n}{-18} < \frac{-144}{-18}
\]

Step2: Simplify both sides

Simplifying the left side, \(\frac{-18n}{-18} = n\). Simplifying the right side, \(\frac{-144}{-18} = 8\). So the solution to the inequality is:
\[
n < 8
\]

Answer:

The solution to the inequality \(-18n > -144\) 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 left (indicating all numbers less than 8).