Chapter 4.9, Problem 16WE

To determine

To find and graph the solutionset of inequality.

Answer to Problem 16WE

The solution set of given inequality is $\left\{x:x=3\right\}$

Explanation of Solution

Given information:

The given inequality is $x^2+9\le 6x$

Calculation:

First write the inequality

  $\begin{array}{l}{x}^2+9\le 6x\\ x^2+9-6x\le 0\left[\text{make one side 0}\right]\\ \left(x-3\right)\left(x-3\right)\le 0\left[\text{factor of the polynomial}\right]\\ {\left(x-3\right)}^2\le 0\end{array}$

The product is non-negative if and only if both factors have opposite sign or at least one factor must be zero.

Here both the factors are same therefore cannot have opposite sign therefore the only condition is factor is equals to zero.

  $\begin{array}{l}x-3=0\\ x=3\end{array}$

The solution set of given inequality is $\left\{x:x=3\right\}$

The graph of the solution set is given below