Chapter 11.3, Problem 2MRE

To determine

To calculate:

Given inequality and graph the solution.

Answer to Problem 2MRE

The solution of the inequality is $-3\le x\le 2$ .

Explanation of Solution

Given information:

Equation:

  $x^2+x\le 6$

Calculation:

Consider the equation $x^2+x\le 6$

  $x^2+x\le 6$

Now find the critical points of the inequality,

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

  $x-2=0$ or $x+3=0$

  $x=2$ or $x=-3$

Now check the intervals in between critical points.

  $\begin{array}{l}x\le -3\\ -3\le x\le 2\\ x\ge 2\end{array}$

The answer is $-3\le x\le 2$ .

The following graph shoes the equation $x^2+x\le 6$ .