Chapter 15.1, Problem 15PSC

To determine

To Find: The solution of the given expression.

Answer to Problem 15PSC

  $x=-3$

Explanation of Solution

Given:

  $x^2+x<6$

Formula Used:

  $\left(x+a\right)\left(x+b\right)=x^2+\left(a+b\right)x+ab$

Calculation:

  $\begin{array}{l}{x}^2+x<6\\ \left(x+a\right)\left(x+b\right)=x^2+\left(a+b\right)x+ab\\ \text{⇒}{x}^2+x-6<0\\ \text{⇒}{x}^2+3x-2x-6<0\\ \text{⇒}x\left(x+3\right)-2\left(x+3\right)<0\\ \text{⇒}\left(x-2\right)\left(x+3\right)<0\\ x=2or-3\\ \text{According to expressoin}\\ x=-3\end{array}$

Conclusion:

Thus, the required solution is $x=-3$ .