Question

solve the inequality 3(2p - 7) > 21

Explanation:

Step1: Divide both sides by 3

To isolate the expression inside the parentheses, we divide both sides of the inequality \( 3(2p - 7) > 21 \) by 3. Since 3 is positive, the direction of the inequality sign remains the same.
\[
\frac{3(2p - 7)}{3} > \frac{21}{3}
\]
Simplifying both sides, we get:
\[
2p - 7 > 7
\]

Step2: Add 7 to both sides

To isolate the term with \( p \), we add 7 to both sides of the inequality \( 2p - 7 > 7 \).
\[
2p - 7 + 7 > 7 + 7
\]
Simplifying both sides, we have:
\[
2p > 14
\]

Step3: Divide both sides by 2

To solve for \( p \), we divide both sides of the inequality \( 2p > 14 \) by 2. Since 2 is positive, the direction of the inequality sign remains the same.
\[
\frac{2p}{2} > \frac{14}{2}
\]
Simplifying both sides, we obtain:
\[
p > 7
\]

Answer:

\( p > 7 \)