Solve the inequality: $12 p+7>139$
A) $p>18$
B) $p>154$
C) $p>12$
D) $p>11$
Answer (1)
Subtract 7 from both sides of the inequality: 139"> 12 p + 7 > 139 becomes 132"> 12 p > 132 .
Divide both sides by 12: 132"> 12 p > 132 becomes 11"> p > 11 .
The solution to the inequality is 11"> p > 11 .
The final answer is 11}"> p > 11 .
Explanation
Understanding the Inequality We are given the inequality 139"> 12 p + 7 > 139 . Our goal is to isolate p on one side of the inequality to find the solution.
Subtracting 7 from Both Sides First, we subtract 7 from both sides of the inequality to get rid of the constant term on the left side:
139 - 7"> 12 p + 7 − 7 > 139 − 7
132"> 12 p > 132
Dividing by 12 Next, we divide both sides of the inequality by 12 to isolate p :
\frac{132}{12}"> 12 12 p > 12 132
11"> p > 11
Final Answer Therefore, the solution to the inequality is 11"> p > 11 . This means that any value of p greater than 11 will satisfy the original inequality.
Examples
Linear inequalities are used in everyday life to determine things like budget constraints. For example, if you have a budget of $200 for groceries and you know that you need to buy at least 5 items, you can use a linear inequality to determine the maximum price you can pay for each item. Similarly, if a phone company charges a fixed monthly fee plus a per-minute charge, you can use a linear inequality to determine how many minutes you can use without exceeding your budget. Understanding and solving linear inequalities helps in making informed decisions in various financial and resource allocation scenarios.
