Write and Graph Inequalities Videos - Free Educational Videos for Students in K - 12

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Graphing linear inequalities


By MathPlanetVideos

Graph the inequality y > 2 - 2x

Graphing Systems of Linear Inequalities - Example 2


By PatrickJMT

In this video, the instructor goes through the steps needed to graph a system of linear inequalities. He discusses slope, shows how to draw the line on the coordinate plane, and explains what section of the graph should be shaded. There is some shadow on the white board which makes it a little more difficult to see at times during the instruction.

Graphing Systems of Linear Inequalities - Example 2


By PatrickJMT

In this video, the instructor goes through the steps needed to graph a system of linear inequalities. He discusses slope, shows how to draw the line on the coordinate plane, and explains what section of the graph should be shaded. There is some shadow on the white board which makes it a little more difficult to see at times during the instruction.

Introduction to graphing inequalities | Two-variable linear inequalities | Algebra I | Khan Academy


By Khan Academy

This video from Khan Academy demonstrates how to graph inequalities. Sal completes some example problems to show you how it's done.

Graph inequalities and check solutions


By Khan Academy

Learn how to graph two-variable linear inequalities.

Graph systems of inequalities and check solutions


By Khan Academy

Sal determines the solution set of the following system: y���������������������2x+1 and y<2x-5 and x>1. He does that by graphing the system and analyzing the graph.

Graph inequalities and check solutions


By Khan Academy

Sal graphs the inequality y<3x+5.

Graph systems of inequalities and check solutions


By Khan Academy

Learn how to graph systems of two-variable linear inequalities.

One-step inequalities


By Khan Academy

In addition to solving the inequality, we'll graph the solution. Remember to swap if you mutiply both sides of the inequality by a negative number.

Graphing inequalities 2 | Algebra Basics | Khan Academy


By Khan Academy

Watch this example of graphing a strict linear inequality. Notice that the first step is converting the inequality into y < mx + b form.

Check solutions of two-variable linear inequalities


By Khan Academy

Sal determines whether the ordered pairs (3,5) and (1,-7) are solutions of the inequality 5x-3y���������������������25. He discussed the problem both algebraically and graphically.

Work Word Problems | MathHelp.com


By MathHelp.com

To solve a polynomial inequality, like the one shown here, our first step is to write the corresponding equation. In other words, we simply change the inequality sign to an equals sign, and we have x^2 – 3 = 9 – x. Next, we solve the equation. Since we have a squared term, we first set the equation equal to 0. So we move the 9 – x to the left side by subtracting 9 and adding x to both sides of the equation. This gives us x^2 + x – 12 = 0. Next, we factor the left side as the product of two binomials. Since the factors of negative 12 that add to positive 1 are positive 4 and negative 3, we have x + 4 times x – 3 = 0. So either x + 4 = 0 or x – 3 = 0, and solving each equation from here, we have x = -4, and x = 3. Now, it’s important to understand that the solutions to the equation, -4 and 3, represent what are called the “critical values” of the inequality, and we plot these critical values on a number line. However, notice that our original inequality uses a greater than sign, rather than greater than or equal to sign, so we use open dots on our critical values of -4 and positive 3. Remember that ‘greater than’ or ‘less than’ means open dot, and ‘greater than or equal to’ or ‘less than or equal to’ means closed dot. Now, we can see that our critical values have divided the number line into three separate intervals: less than -4, between -4 and 3, and greater than 3. And here’s the important part. Our next step is to test a value from each of the intervals by plugging the value back into the original inequality to see if it gives us a true statement. So let’s first test a value from the “less than -4” interval, such as -5. If we plug a -5 back in for both x’s in the original inequality, we have -5 squared – 3 greater than 9 minus a -5, which simplifies to 25 – 3 greater than 9 + 5, or 22 greater than 14. Since 22 greater than 14 is a true statement, this means that all values in the interval we’re testing are solutions to inequality, so we shade the interval. Next, we test a value from the “between -4 and 3” interval, such as 0. If we plug a 0 back in for both x’s in the original inequality, we have 0 squared – 3 greater than 9 – 0, which simplifies to 0 – 3 greater than 9, or -3 greater than 9. Since -3 greater than 9 is a false statement, this means that all values in the interval we’re testing are not solutions to inequality, so we don’t shade the interval. Next, we test a value from the “greater than 3” interval, such as 4. If we plug a 4 back in for both x’s in the original inequality, we have 4 squared – 3 greater than 9 – 4, which simplifies to 16 – 3 greater than 5, or 13 greater than 5. Since 13 greater than 5 is a true statement, this means that all values in the interval we’re testing are solutions to inequality, so we shade the interval. Finally, we write the answer that’s shown on our graph in set notation. The set of all x’s such that x is less than -4 or x is greater than 3.

Constraint solution sets of systems of linear inequalities


By Khan Academy

Given the graph of a system of inequalities, Sal finds the x-values that make the ordered pair (x,-2) a solution of the system, which is the solution set constrained to y=-2. Then he solves a similar problem where x is constrained to 4.

Two-variable linear inequalities word problems


By Khan Academy

Sal is given the graph of a two-variable linear inequality that models a context about dog biscuits! He analyzes it to learn about the context and to check a possible solution.

Constraint solution sets of two-variable linear inequalities


By Khan Academy

Sal determines which x-values make the ordered pair (x,-7) a solution of 2x-7y<25. He also solves a similar problem where the inequality is given as a graph.

Systems of linear inequalities word problems


By Khan Academy

Sal is given the graph of a two-variable linear inequality that models a context about chopping vegetables. He analyzes the solution set of the system in terms of the context.