Chapter 3.5, Problem 2STP

For Exercises $1-6,$ choose the correct letter.

What set represents the solution of $15<-9j-3?$

F. $j<-2$

G. $\{-2\}$

H. $\{j\mid j>-2\}$

I. $\{j\mid j<-2\}$

To determine

To find the set that represents the solution of the inequality $15<-9j-3$ .

Answer to Problem 2STP

Solution is $\left\{j/j<-2\right\}$ and option I is correct.

Explanation of Solution

Given:

  $15<-9j-3$

Concept used:

When multiplying or dividing each side of an inequality by the same negative number, the direction of the inequality symbol must be reversed to produce an equivalent inequality.

Calculation:

  $15<-9j-3$

Adding 3 on both sides, we get

  $\begin{array}{l}15+3<-9j-3+3\\ \Rightarrow 18<-9j\end{array}$

Dividing by $-9$ on both sides, we get

  $\begin{array}{l}\frac{18}{-9}>\frac{-9j}{-9}\\ \Rightarrow -2>j\\ \Rightarrow j<-2\end{array}$

Therefore, set-builder form is,

  $\left\{j/j<-2\right\}$

Hence option I is correct.