Chapter 1.8, Problem 2CFU

To determine

To describe: the process used to graph the given inequality.

Answer to Problem 2CFU

The process is as follows:

1. Identify the parts of given inequality.
2. Solve the parts of the equation in terms of the variables.
3. Graph the line depending on the inequality.
4. If the inequality has $\le \text{ or}\ge$ sign, then solid line will be used to graph the line. If the inequality has $\text{< or >}$ sign, then dotted line will be used to graph the line

Explanation of Solution

Given information:

The inequality is shown below.

  $-3\le 2x+y<7$

Calculation:

There are two parts of this inequality

  $\begin{array}{l}\text{First part: }-3\le 2x+y\\ \text{Second part: }2x+y<7\end{array}$

Solve the both parts of the equation in terms of y or x as shown below.

  $\begin{array}{l}\text{First part: }-3-2x\le y\\ \text{Second part: }y<7-2x\end{array}$

Since, the first part of inequality has less than or equal to sign $(\le )$ , so solid line will be used.

Since, the second part of inequality has less than sign $(<)$ , so dotted line will be used.

Now, line to graph (first part) , $y=-3-2x$ with the solid line and line to graph (second part), $y=7-2x$ with dotted line.