Question

1. ( 5(6p - 4) > -260 )

Explanation:

Step1: Divide both sides by 5

To isolate the expression inside the parentheses, we divide both sides of the inequality \(5(6p - 4)>-260\) by 5. This gives us \(\frac{5(6p - 4)}{5}>\frac{-260}{5}\), which simplifies to \(6p - 4>-52\).

Step2: Add 4 to both sides

Next, we add 4 to both sides of the inequality \(6p - 4>-52\) to isolate the term with \(p\). So, \(6p - 4 + 4>-52 + 4\), which simplifies to \(6p>-48\).

Step3: Divide both sides by 6

Finally, we divide both sides of the inequality \(6p>-48\) by 6 to solve for \(p\). This gives us \(\frac{6p}{6}>\frac{-48}{6}\), which simplifies to \(p>-8\).

Answer:

The solution to the inequality \(5(6p - 4)>-260\) is \(p > - 8\). On the number line, this would be represented by an open circle at \(-8\) and an arrow pointing to the right (towards positive infinity).