Question

Graph the solution set. $$ 3 x-5 y>0 $$

   Graph the solution set.
$$
3 x-5 y>0
$$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 3, Problem 107

Instant Answer

Solved by Expert James Kiss

02/05/2022

Step 1

We can do this by adding $5y$ to both sides of the inequality to isolate the $y$ term on one side: $$3x - 5y > 0 \Rightarrow 3x > 5y$$ Show more…

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Graph the solution set. $$ 3 x-5 y>0 $$

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Key Concepts

Test Point Method

The test point method involves selecting a point not on the boundary line (commonly the origin, if it is not on the boundary) and substituting it into the inequality to determine which side of the boundary line satisfies the inequality. This step helps ensure that the correct half-plane is shaded in the final graph.

Boundary Lines

The boundary line is derived from the equality version of the inequality (e.g., 3x - 5y = 0). This line is either dashed or solid depending on whether the inequality is strict (>) or non-strict (?). The treatment of the boundary is essential for accurately representing the solution set on the graph.

Linear Inequalities

Linear inequalities involve expressions of the form ax + by > c (or ?, <, ?) where the solution set includes all points (x,y) that make the inequality true. They model many real-world scenarios and are an extension of linear equations with an inequality sign rather than an equality.

Graphing the Solution Set

Graphing a linear inequality requires shading the region of the coordinate plane that satisfies the inequality. This process involves first plotting the boundary, which is the line obtained by replacing the inequality with an equality, and then determining which side of the line represents the solution set.

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