Solve this inequality: $3 p-6>21$.
A) $p>-9$
B) $p>-5$
C) $p>9$
D) $p>5$
Answer (1)
Add 6 to both sides of the inequality: 21 + 6"> 3 p − 6 + 6 > 21 + 6 , which simplifies to 27"> 3 p > 27 .
Divide both sides by 3: \frac{27}{3}"> 3 3 p > 3 27 .
Simplify to isolate p : 9"> p > 9 .
The solution to the inequality is 9}"> p > 9 .
Explanation
Understanding the Problem We are given the inequality 21"> 3 p − 6 > 21 and asked to solve for p . Our goal is to isolate p on one side of the inequality to find the solution set.
Adding 6 to Both Sides First, we add 6 to both sides of the inequality to eliminate the constant term on the left side: 21 + 6"> 3 p − 6 + 6 > 21 + 6
Simplifying the Inequality This simplifies to: 27"> 3 p > 27
Dividing by 3 Next, we divide both sides of the inequality by 3 to isolate p :
\frac{27}{3}"> 3 3 p > 3 27
Solving for p This simplifies to: 9"> p > 9
Final Answer Therefore, the solution to the inequality 21"> 3 p − 6 > 21 is 9"> p > 9 . This corresponds to option C.
Examples
Imagine you're saving money for a new video game that costs $21. You already owe your friend $6, and you earn $3 per hour at your part-time job. The inequality 21"> 3 p − 6 > 21 helps you determine how many hours ( p ) you need to work to have enough money to buy the game after paying back your friend. Solving this inequality shows you that you need to work more than 9 hours to achieve your goal. Understanding and solving linear inequalities is useful in many real-life situations involving budgeting, planning, and resource allocation.
