Chapter 6.1, Problem 74STP

To determine

To find: The inequality of the equation $x^2-6x\le 16$ .

Answer to Problem 74STP

The inequalities of the equation is $x\le -2$ or $x\le 8$ .

Explanation of Solution

Given information:

The given equation is $x^2-6x\le 16$ .

Calculation:

Calculate the inequality of the equation.

  $x^2-6x\le 16$

Subtracting both sides by 16.

  $\begin{array}{l}{x}^2-6x-16\le 16-16\\ x^2-6x-16\le 0\end{array}$

Now, using the method term splitting to further solve equation.

  $\begin{array}{c}{x}^2-8x+2x-16\le 0\\ x(x-8)+2(x-8)\le 0\\ (x+2)(x-8)\le 0\end{array}$

Thus,

  $(x+2)\le 0$ or, $(x-8)\le 0$

So,

  $x\le -2$ or, $x\le 8$

Therefore, the inequalities of the equation are $x\le -2$ or $x\le 8$ .