Chapter 4.4, Problem 55AYU

To determine

To calculate:

The solution of following inequality equation:

  $3\left(x^2-2\right)<2{\left(x-1\right)}^2+x^2$

Answer to Problem 55AYU

The solution of the inequality equation $3\left(x^2-2\right)<2{\left(x-1\right)}^2+x^2$ is $x<2$ .

Explanation of Solution

Given information:

  $3\left(x^2-2\right)<2{\left(x-1\right)}^2+x^2$

Calculation:

The given equation is:

  $\begin{array}{l}3\left(x^2-2\right)<2{\left(x-1\right)}^2+x^2\\ 3\left(x^2-2\right)-2{\left(x-1\right)}^2-x^2=0\\ 3x^2-6-2\left(x^2-2x+1\right)-x^2=0\\ 3x^2-6-2x^2+4x-2-x^2=0\\ -8+4x=0\\ x=2\end{array}$

Hence, the inequality is solved for $x<2$ .