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Chapter 4: Q. 515 (page 557)

Write the inequality shown by the shaded region in the graph with the boundary line x+y=3.

Short Answer

Expert verified

x+y>3

Step by step solution

01

Step 1. Given information 

We have been given a graph:

We have to write the inequality shown by the graph.

02

Step 2. Find the inequality representing the shaded region 

The line x+y=3is the boundary line.

On one side of the line are the points with x+y>3and on the other side of the line are the points with x+y<3.

Let鈥檚 test the point (0, 0) and see which inequality describes its side of the boundary line.

At (0, 0) , which inequality is true:

x+y>30+0>?30鈮�3 or x+y<30+0<?30<3

So the side with (0, 0) is the side where x+y<3.

We need to find the inequality for the region that does not contain (0,0).

Since the boundary line is graphed as a solid line, the inequality includes an equal sign.

The graph shows the solution to the inequality x+y>3.

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