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Chapter 4: Q. 4.141 (page 550)

Write the inequality shown by the shaded region in the graph with the boundary line x鈭�4y=8

Short Answer

Expert verified

The inequality shown by the graph is x-4y鈮�8.

Step by step solution

01

Step 1. Given Information

We are given an equation x鈭�4y=8and a graph,

02

Step 2. Finding the inequality 

The line x鈭�4y=8is the boundary line. On one side of the line are the points with x鈭�4y>8and on the other side of the line are the points with x鈭�4y<8.

Checking the inequality with point 0,0,

x鈭�4y>80鈭�4(0)>80>8

False.

03

Step 3. Finding the inequality 

Checking the inequality with point 0,0,

localid="1647587517869" x鈭�4y<80鈭�4(0)<80<8

True.

Since x-4y<8is true for the point (0,0)which is the part of shaded region, hence shaded region is the solution for the inequality x-4y<8

Also, the boundary line is graphed with a solid line, the inequality includes the equal sign.

x-4y鈮�8

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