Chapter 3, Problem 19PTTS

To determine

To find: The inequalities.

Answer to Problem 19PTTS

The connect inequalities is $-4x-5<7$ and the connect option is G.

Explanation of Solution

Given information:

  

Calculation: From the graph it is clear the solution should be, $x>-3$

Let’s find the connect inequality.

  $\begin{array}{l}\text{F}\text{. }2x+10<16,\\ \Rightarrow 2x<16-10\\ \Rightarrow 2x<6\\ \Rightarrow x<3\end{array}$

  $\begin{array}{l}\text{G}\text{. }-4x-5<7\\ \Rightarrow -4x<7+5\\ \Rightarrow -4x<12\\ \Rightarrow -x<3\\ \Rightarrow x>-3\end{array}$

  $\begin{array}{l}\text{H}\text{. }-3x+8<-1\\ \Rightarrow -3x<-1-8\\ \Rightarrow -3x<-9\\ \Rightarrow -x<-3\\ \Rightarrow x<3\end{array}$

  $\begin{array}{l}\text{I}\text{. }4-2x>10\\ \Rightarrow -2x>10-4\\ \Rightarrow -2x>6\\ \Rightarrow x<-3\end{array}$

Hence, The connect inequalities is $-4x-5<7$ and the connect option is G.