Chapter 3.5, Problem 17PPE

To determine

To write: The solution of given inequality in set-builder notation.

Answer to Problem 17PPE

The set-builder notation, the solution is $\{p\mid p\ge 1\}$

Explanation of Solution

Given information:

The inequality,

  $2\left(3p–11\right)\ge –16$

Calculation:

Consider the inequality,

  $2\left(3p–11\right)\ge –16$

To Solve the inequality, move all the constants to the right and keep the variable in the left.

The inequality can be solved as follows:

  $2\left(3p–11\right)\ge –16$ Consider the original inequality

  $\frac{2(3p-11)}{2}\ge \frac{-16}{2}$ Divide each side by 2

  $3p-11\ge -8$ Simplify

  $3p-11+11\ge -8+11$ Add 11 to each side

  $3p\ge 3$ Simplify

  $\frac{3p}{3}\ge \frac{3}{3}$ Divide each side by 3

  $p\ge 1$ Simplify

Therefore, the solution is $p\ge 1$ .

The set builder from describes a properties of an element must have to be included in a set.

In set-builder notation, the solution is $\{p\mid p\ge 1\}$