Chapter 8.2, Problem 4BCYP

To determine

To Find:

The inequality of $2^{x+2}\ge \frac{1}{32}$ .

Answer to Problem 4BCYP

The simplified solution is $x\ge -7$ .

Explanation of Solution

Given information:

The given function is $2^{x+2}\ge \frac{1}{32}$ .

Consider $2^{x+2}\ge \frac{1}{32}$ ,

  $\begin{array}{l}{2}^{x+2}\ge \frac{1}{2^5}\\ 2^{x+2}\ge 2^{-5}\end{array}$

By property of inequality for exponential functions,

  $\begin{array}{l}x+2\ge -5\\ x\ge -5-2\\ x\ge -7\end{array}$

Therefore, the simplified solution is $x\ge -7$ .