Chapter 13.4, Problem 6PSB

To determine

To find: The union of the solution sets of the inequalities.

Answer to Problem 6PSB

The union of the solution sets of the two inequalities by the graph is shown below.

Explanation of Solution

Given:

The given inequalities are:

  $\begin{array}{c}x+y>4\\ y<2x-6\end{array}$

Graph is described as:

  $\begin{array}{c}x+y>4\\ 0+0>4\left[\text{false}\right]\\ y<2x-6\\ 0<2\left(0\right)-6\left[\text{false}\right]\end{array}$

The shaded region is the union of area above of the graph line of $x+y=4$ and the area right of the graph line of $y=2x-6$ .

  

The graph is given as:

  

Therefore, the union of the solution sets of the two inequalities by the graph is shown above.