Think About It After graphing the boundary of the inequality x+y<3 , explain how you decide on w

step 1 Okay, so we have this inequality right here and Problem asks us basically when we graph the boun

Think About It After graphing the boundary of the inequality...

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Key Concepts

Graphing Linear Inequalities

Graphing linear inequalities involves representing a linear boundary on the coordinate plane and then shading one of the half-planes defined by that boundary. This process visualizes all the points that satisfy the inequality.

Boundary Representation

The boundary line, which is determined by setting the inequality as an equality, serves as the dividing line between the two regions on the graph. Whether this line is drawn as dashed or solid depends on whether the inequality is strict or inclusive.

Test Point Method

The test point method is used to identify which side of the boundary line contains the solution set. By choosing a point not on the boundary and substituting its coordinates into the inequality, you can verify if the inequality holds, indicating that the region containing that point is part of the solution set.

Solution Set Identification

The solution set of a linear inequality is the collection of all points on the appropriate side of the boundary that satisfy the inequality. Once the correct side is determined using methods such as the test point, this region is highlighted as the set of possible solutions.

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