Solve this inequality: [tex]$3 p-6\ \textgreater \ 21$[/tex].
A) [tex]$p\ \textgreater \ 5$[/tex]
B) [tex]$p\ \textgreater \ 9$[/tex]
C) [tex]$p\ \textgreater \ -5$[/tex]
D) [tex]$p\ \textgreater \ -9$[/tex]
Answer (2)
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 find the solution: 9"> p > 9 .
The solution to the inequality is 9}"> p > 9 .
Explanation
Understanding the Inequality We are given the inequality 21"> 3 p − 6 > 21 . Our goal is to isolate p to find the solution.
Adding to Both Sides First, we add 6 to both sides of the inequality to eliminate the -6 on the left side: 21 + 6"> 3 p − 6 + 6 > 21 + 6
Simplifying the Inequality This simplifies to: 27"> 3 p > 27
Dividing to Isolate p Next, we divide both sides of the inequality by 3 to solve for p :
\frac{27}{3}"> 3 3 p > 3 27
Finding the Solution This simplifies to: 9"> p > 9 So the solution to the inequality is 9"> p > 9 .
Examples
Imagine you're saving money for a new bicycle that costs $21. You already have a plan to earn $6 by doing chores. If you earn $3 per hour at a part-time job, this inequality helps you determine how many hours (p) you need to work to afford the bicycle. Solving it shows you need to work more than 9 hours.
To solve the inequality 21"> 3 p − 6 > 21 , we find that 9"> p > 9 after simplifying. The correct answer is option B. This indicates the values of p must be greater than 9.
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