Chapter 5.1, Problem 12MRE

To determine

To find: Solution set of each inequality.

Answer to Problem 12MRE

Solution set of given inequality is $u>3$ or $u\le 2$ .

Explanation of Solution

Given information:

  $-2u<-6$ or $u-1\le 1$

  $-2u<-6$ or $u-1\le 1$

Taking first expression

We get

  $\begin{array}{l}-2u<-6\\ \Rightarrow -2u+2u<-6+2u\\ \Rightarrow 0<2u-6\\ \Rightarrow 2u-6>0\\ \Rightarrow 2u-6+6>0+6\\ \Rightarrow 2u>6\\ \Rightarrow \frac{2u}{2}>\frac{6}{2}\\ \Rightarrow u>3\end{array}$

Taking second expression

We get

  $\begin{array}{l}u-1\le 1\\ \Rightarrow u-1+1\le 1+1\\ \Rightarrow u\le 2\end{array}$

Therefore,

Solution set of given inequality is $u>3$ or $u\le 2$ .