Chapter 0.2, Problem 6QR

To determine

To find: Solve the inequality for $x$ .

Answer to Problem 6QR

The solution of given inequality is $x=-3$ or $x=3$ .

Explanation of Solution

Given information:

The given inequality is $9-x^2\ge 0$ .

Calculation:

Subtract 9 on both sides:

  $\begin{array}{l}9-x^2-9\ge -9\\ -x^2\ge -9\\ x^2\ge 9\\ x^2-9\ge 9-9\\ x^2-9\ge 0\end{array}$

The left-hand side is zero when either factor is zero.

  $x+3=0$ or $x=-3$

  $x-3=0$ or $x=3$ .

This is the expression for $x$ .