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:

\( p > 7 \)