Chapter 7.4, Problem 7E

Solution

To Graph: The given inequality by using the hand sketch and state the boundary region.

  $x\le 4$

The graph of the inequality is shown as below,

  

Given Information:

The inequality is defined as,

  $x\le 4$

Explanation:

Consider the given inequality,

  $x\le 4$

Replacing the inequality symbol with the = symbol, the equation for the boundary is  $x=4$ ,That is a vertical line.

The boundary point is included if the inequality containing $\le \text{ or }\ge$ symbols and the boundary point is excluded if the symbols $<\text{ or }>$ is used.

As the less then equal to symbol was used, then the boundary is included in the graph and drawing it by using solid line.

To determine the half-plane to be shaded, use a test point not on the boundary, say  $\left(0,0\right)$ .

Since, $0\le 4$

The statement is true so shade the half-plane where  $\left(0,0\right)$  is located.

The graph will be:

  

Hence, the required graph is shown above.