Chapter 5.2, Problem 2QR

To determine

To find : Exact solution to the inequality $3x^2-6>0$ .

Answer to Problem 2QR

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

Explanation of Solution

Given information :

The inequality is $3x^2-6>0$ .

Calculation :

Consider the given inequality:

  $3x^2-6>0$

Solve the above inequality for $x$ :

  $\begin{array}{l}3x^2-6>0\\ 3x^2-6+6>0+6\text{ (Adding 6 on both sides)}\\ 3x^2>6\\ \frac{3x^2}{3}>\frac{6}{2}\text{ (Divide both sides by 3)}\\ x^2>2\mathrm{......}\text{ (1)}\end{array}$

Since, for any $x^2>a$ , then $x<-\sqrt{a}$ and $x>\sqrt{a}$ .

Therefore, the solution of the inequality is $x<-\sqrt{2}$ and $x>\sqrt{2}$ .

Hence,

The solution of the inequality is $x<-\sqrt{2}$ and $x>\sqrt{2}$ .