Graph the inequality 2 x + 3 y < 6 2x+3y<6 .

Welcome back, everyone. So in this practice problem, we're going to graph this inequality that's shown to us, 2x plus 3y is less than 6. So this is clearly a linear inequality. Let's go ahead and just take a look at our steps here. So the first thing we have to do is just figure out whether we're dealing with a solid or a dashed line, and then we're gonna have to graph that line. And remember, we do this by switching this inequality symbol and kind of just pretending that there's an equal sign here. So let's go ahead and do this. I'm actually just gonna write this down here because 2x plus 3y is less than 6 may not be super easy to graph right now because it's in standard form. So one thing we can do here is we can just sort of or switch it into slope intercept form. So to do that, remember, I just have to isolate for y. So I'm gonna subtract 2 x from both sides to basically bring it over. I'm gonna subtract 2 x, and then I have that 3 y is less than negative 2 x plus 6. Now, I just divide by 3 on both sides. Now, unfortunately, this leads to a little bit of a fraction, but that's okay. So we're just gonna have to divide 3 by have to divide every one of the terms by 3. What you'll see here is that we're gonna get y is less than negative 2 thirds x plus 6. So we see that this is kind of like in in slope intercept form, y equals mx plus b. And actually, I'm sorry, this shouldn't be 6 because 6 divided by 3 ends up being 2. So this actually ends up being a little bit easier to graph because all we're gonna have to do here is take a look at the y intercept of 2. We know that we're gonna have a slope of negative 2 thirds, which means we go down 2 and to the right 3. So we go down 2 and to the right 3, and that's basically gonna be our line. And we just connect this, like this. So I just have to connect these points kind of like that. Alright? Now remember, are we dealing with a solid or dashed line? Well, remember, that just comes down to the symbol. And because we just have a less than symbol, not a less than or equal to symbol, we're going to use a dash line over here. All right. So this is going to be a dash line that goes through these points. All right. So this is going to be the equation of our line. That's what the graph looks like. Now we're going to move on to the second step over here, which is testing a point. So we're going to test a point just to make sure on either side of the line. We're just going to basically plug the x y values into the inequality symbol. It's always best to use a point that's on the x or y axis because it makes the math a little bit easier. So one thing I can do here is I'm just gonna test this point over here, which is 0 comma negative one. So 0 comma negative one. So So let's go ahead and do that here. If I plug in the point 0 comma negative 1 into this inequality, what do I get? Well, I'm gonna get the 2 times 0. So I'm just gonna use the the point 0 comma negative 1. I'm gonna get 2 times 0, which works out to 0, plus 3 times negative one. Is that less than 6? Alright? Well, clearly, what we can see here is that this works out to negative 3, and negative 3 clearly is less than 6. That is a true statement. Alright? So now that moves on to the 3rd step. We move on to the 3rd step, which says that if the point makes the inequality true, which is what we had here, then we're gonna shade the side with that includes that point with that point. Alright? So we have that as less than. So, I mean, in other words, it's just gonna be all of this area that's over here. That's gonna be the those are gonna be the the points that satisfy our inequality. You also could have just used the shortcut that for linear equations, remember, once you get it into slope intercept form like this, if it's less than, then it's going to be shading below that line. You also totally could have used that. Alright? So these are the numbers or the points that would satisfy your inequality. Thanks for watching, and I'll see you in the next one.

Table of contents

Skip topic navigation

1. Whole Numbers1h 55m

Multiplying Whole Numbers
46m

Dividing Whole Numbers
21m

Long Division
36m

Exponents
10m

2. Integers1h 7m

Introduction to Integers
16m

Multiplying Integers
24m

Exponential Expressions
10m

Dividing Integers
16m

3. Introduction to Solving Equations and Problem Solving Coming soon

4. Fractions1h 29m

Intro To Fractions and Mixed Numbers
44m

Simplifying Fractions
45m

5. Decimals1h 20m

Introduction To Decimals
27m

Rounding Decimals
12m

Adding And Subtracting Decimals
41m

6. Ratio, Proportion, and Percent2h 3m

Ratios and Rates
35m

Proportions
34m

Solving Percent Problems With Equations
16m

Applications of Percent
36m

7. Graphing and Introduction to Statistics Coming soon

8. Geometry49m

Square Roots and The Pythagorean Theorem
29m

The Circle
20m

9. Measurement Coming soon

10. Linear Equations and Inequalities6h 13m

The Distributive Property
17m

Review: Addition and Subtraction Properties of Equality
41m

Review: Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Introduction to Problem Solving
37m

Formulas
21m

Review: Percent Problem Solving
59m

Mixture Problem Solving
43m

Linear Inequalities in One Variable
46m

11. Graphing Linear Equations3h 17m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
38m

Point Slope Form
22m

12. Systems of Linear Equations1h 43m

Solving Systems of Linear Equations by Graphing
41m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

13. Exponents and Polynomials3h 55m

Review: Evaluating Exponents
29m

The Product Rule
10m

Intro to the Power Rules
18m

The Power of a Quotient Rule
18m

Negative Exponents
28m

The Quotient Rule
13m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
33m

Special Products
34m

14. Factoring Polynomials2h 42m

Factoring by Greatest Common Factor & Grouping
37m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Factoring Special Products
20m

Sum & Difference of Cubes
12m

Quadratic Equations & Applications
41m

15. Rational Expressions and Equations3h 13m

Simplifying Rational Expressions
39m

Multiplying And Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
19m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

Rational Equations
44m

16. Relations and Functions2h 9m

Introduction to Relations and Functions
57m

Function Notation
15m

Graphing Common Functions
5m

Composition of Functions
24m

Direct & Inverse Variation
27m

17. Inequalities and Absolute Value2h 52m

Set Operations and Compound Inequalities
42m

Absolute Value Equations
38m

Absolute Value Inequalities
39m

Linear Inequalities in Two Variables
28m

Systems of Linear Inequalities
23m

18. Roots, Radicals, and Complex Numbers3h 57m

Introduction to Radical Expressions
47m

Simplifying Radical Expressions
47m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
53m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

19. Quadratic Equations and Functions3h 1m

The Square Root Property
25m

Completing the Square
26m

The Quadratic Formula
40m

Graphing Quadratic Equations
1h 28m

20. Exponential and Logarithmic Functions2h 31m

Introduction to Inverse Functions
25m

Exponential Functions
35m

Introduction to Logarithmic Functions
33m

Properties of Logarithms
55m

21. Conic Sections and Systems of Nonlinear Equations2h 24m

Parabolas
35m

Graphing Circles
32m

Ellipses
35m

Hyperbolas
41m

22. Sequences, Series, and the Binomial Theorem1h 45m

Introduction to Sequences
40m

Arithmetic Sequences
27m

Geometric Sequences
26m

Factorials
11m

17. Inequalities and Absolute Value

Linear Inequalities in Two Variables

Prealgebra, Beginning Algebra, & Intermediate Algebra

17. Inequalities and Absolute Value

Linear Inequalities in Two Variables

Previous problemNext problem

Struggling with Prealgebra, Beginning Algebra, & Intermediate Algebra?

Join thousands of students who trust us to help them ace their exams!

Multiple Choice

Graph the inequality $2 x plus 3 y is less than 6$ .

Inequality graph

Inequality symbol

0 Comments

Previous problemNext problem

5:47m

Watch next

Master Intro to Linear Inequalities in Two Variables with a bite sized video explanation from Jennifer Canizales

Struggling with Prealgebra, Beginning Algebra, & Intermediate Algebra?

Graph the inequality 2x+3y<62x+3y<6.

Watch next

Graph the inequality $2 x plus 3 y is less than 6$ .