Solving The Inequality 12P + 7 ≤ 139

Solved 1. Solve the inequality 12p+7> 139 B. p> 12 C.p>11 from www.chegg.com

Introduction

Inequalities are mathematical statements that compare two values using a less than, greater than, less than or equal to, or greater than or equal to sign. Solving inequalities involves finding the range of values that satisfy the given inequality. In this article, we will focus on solving the inequality 12p + 7 ≤ 139.

Understanding the Inequality

The inequality 12p + 7 ≤ 139 can be read as "twelve times the value of p plus seven is less than or equal to 139". To solve this inequality, we need to isolate the variable p on one side of the inequality.

Step 1: Subtract 7 from both sides

We can start by subtracting 7 from both sides of the inequality: 12p + 7 - 7 ≤ 139 - 7 Simplifying the left-hand side, we get: 12p ≤ 132

Step 2: Divide both sides by 12

To isolate p, we need to divide both sides of the inequality by 12: 12p/12 ≤ 132/12 Simplifying, we get: p ≤ 11

Solution

Therefore, the solution to the inequality 12p + 7 ≤ 139 is: p ≤ 11 This means that any value of p that is less than or equal to 11 will satisfy the inequality.

Graphical Representation

We can also represent the solution graphically on a number line. To do this, we plot a closed circle at 11 and shade the region to the left of the circle, since any value less than or equal to 11 satisfies the inequality.

Graphical representation of the solution

Conclusion

Inequalities are important in mathematics and have numerous applications in real-life situations. Solving inequalities involves finding the range of values that satisfy the given inequality. In the case of the inequality 12p + 7 ≤ 139, we found that any value of p that is less than or equal to 11 satisfies the inequality.