Question

Graph the solution set. $$ 5 x-4 y<-3 $$

   Graph the solution set.
$$
5 x-4 y<-3
$$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 3, Problem 34

Instant Answer

Solved by Expert Jennifer Stoner

03/11/2023

Step 1

To do this, we can add 4y to both sides and then divide by -4 to isolate y: $$ 5x - 4y < -3 \implies 4y > 5x + 3 \implies y > \frac{5}{4}x + \frac{3}{4} $$ Show more…

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Graph the solution set. $$ 5 x-4 y<-3 $$

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Key Concepts

Test Point Method

The test point method involves selecting a point not on the boundary line and substituting it into the original inequality to determine which side of the line satisfies the condition. This helps in deciding the area of the graph that should be shaded to represent the solution set.

Linear Inequality

A linear inequality is similar to a linear equation, but instead of an equal sign, it uses inequality signs (such as <, >, ?, or ?) to describe a relationship that holds over a range of values. Understanding linear inequalities is fundamental in determining regions of solutions rather than a single value.

Graphing Linear Inequalities

Graphing linear inequalities involves first graphing the corresponding linear equation (by converting the inequality to an equality) to project a boundary line, and then shading the region that satisfies the inequality. This method provides a visual of all possible solutions to the inequality.

Boundary Line

The boundary line of a linear inequality is obtained by converting the inequality into its corresponding linear equation. It acts as a divider for the coordinate plane into two regions, and whether the line itself is included in the solution set depends on whether the inequality is strict (using < or >) or inclusive (using ? or ?).

Slope-Intercept Form

Converting a linear equation to the slope-intercept form (y = mx + b) simplifies graphing by clearly presenting the slope and the y-intercept. This form is especially useful when graphing the boundary line of a linear inequality, as it allows for an accurate and quick sketch of the line.

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