Chapter 3.5, Problem 18PPE

To determine

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

Answer to Problem 18PPE

The set-builder notation, the solution is $\{k\mid k<-13\}$

Explanation of Solution

Given information:

The inequality,

  $3\left(2k+12\right)<–42$ .

Calculation:

Consider the inequality,

  $3\left(2k+12\right)<–42$

To solve the inequality, more all the constants to the right and keep the variable in the left.

The inequality can be solved as follows:

  $3\left(2k+12\right)<–42$

Consider the original inequality

  $\frac{3(2k+12)}{3}<\frac{-42}{3}$ Divide each side by 3

  $2k+12<-14$ Simplify

  $2k+12-12<-14-12$ subtract each side by 12

  $2k<-26$ Simplify

  $\frac{2k}{2}<\frac{-26}{2}$ Divide each side by 2

  $k<-13$ Simplify

Therefore, the solution is $[k<-13]$ .

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 $\{k\mid k<-13\}$