Chapter 2.4, Problem 34WE

To determine

The solution set of each open sentence.

Answer to Problem 34WE

  $\text{The solution set is {t: t < 6}}\text{.}$

Explanation of Solution

Given:

The given open sentence is:

  $\left|t\right|>\left|2t-6\right|$

Calculation:

The solution of the given open sentence will be:

  $\begin{array}{l}\left|t\right|>\left|2t-6\right|\\ \frac{\left|t\right|}{\left|2t-6\right|}>1\\ \left|\frac{t}{2t-6}\right|>1\\ \text{Write in form of disjunction:}\\ \frac{t}{2t-6}<-1\text{ or }\frac{t}{2t-6}>1\\ t<-2t+6\text{ or t > 2t - 6}\\ 3t<6\text{ or - t > - 6}\\ t<2\text{ or t < 6}\\ \text{The solution set is {t: t < 6}}\text{.}\end{array}$