Chapter 11.3, Problem 3MRE

To determine

To calculate:

Given inequality and graph the solution.

Answer to Problem 3MRE

The solution of the inequality is $-4\le x<2$ .

Explanation of Solution

Given information:

Equation:

  $2\le \frac{x}{2}+4<5$

Calculation:

Consider the equation $2\le \frac{x}{2}+4<5$

Now simplify all parts of the inequality,

  $\begin{array}{l}2\le \frac{x}{2}+4<5\\ 2\le \frac{1}{2}x+4<5\\ 2+-4\le \frac{1}{2}x+4+-4<5+-4\\ -2\le \frac{1}{2}x<1\end{array}$

Now divide all parts,

  $\begin{array}{l}\frac{-2}{\frac{1}{2}}\le \frac{\frac{1}{2}x}{\frac{1}{2}}<\frac{1}{\frac{1}{2}}\\ -4\le x<2\end{array}$

The answer is $-4\le x<2$ .

The following graph shoes the equation $2\le \frac{x}{2}+4<5$ .