Chapter 5.2, Problem 1QR

To determine

To find : Exact solution to the inequality $2x^2-6<0$ .

Answer to Problem 1QR

The solution of the inequality is $-\sqrt{3}<x<\sqrt{3}$ .

Explanation of Solution

Given information :

The inequality is $2x^2-6<0$ .

Calculation :

Consider the given inequality:

  $2x^2-6<0$

Solve the above inequality for $x$ :

  $\begin{array}{l}2x^2-6<0\\ 2x^2-6+6<0+6\text{ (Adding 6 on both sides)}\\ 2x^2<6\\ \frac{2x^2}{2}<\frac{6}{2}\text{ (Divide both sides by 2)}\\ x^2<3\end{array}$

Take square root on both sides and write the inequality as compound inequality.

  $\begin{array}{l}-\sqrt{3}<\sqrt{x^2}<\sqrt{3}\\ -\sqrt{3}<x<\sqrt{3}\end{array}$

Hence,

The solution of the inequality is $-\sqrt{3}<x<\sqrt{3}$ .