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### Course: Algebra 1>Unit 7

Lesson 1: Checking solutions of two-variable inequalities

# Testing solutions to inequalities

Sal checks if the ordered pairs (3,5) and (1,-7) are solutions of the inequality 5x-3y≥25. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• why are these comments from yeaarss ago?
• The pages default to top rank questions and answers, these are often older. If you want to see the new comments, select sort by newest first.
• how would you graph y>3/2x?
• Since there is no y-intercept you must know that it means that the y-intercept is 0. This means that the line passes through (0,0). So, your equation is now y>3/2x+0. Now graph it and shade. you should have a line that passes through (0,0) with a slope of 3/2 and the shading should be everything above the line. Your welcome and please vote.
• At , Sal said that is not true that 0 is greater than or equal to 25! Wouldn't he flip the inequality sign?
(1 vote)
• No, he can't just flip the inequality. We only flip the inequality if we multiply or divide the entire inequality by a negative value.

The point Sal tested makes the inequality false. This means it is not a solution to the inequality.

Hope this helps.
• What Grade would this Math be?
• That's a great question! I would say that it would be 8th grade because it's in Algebra 1! I talked that one to David severin as well!
• Twenty-six does bigger than twenty-five,but is not equal to it. So why can we say like that?
• The inequation in this video uses the bigger or equal sign, which tests as true if the first number be bigger or equal to the second. In this case, 26 is bigger than 25, so the resulting statement is true.
• Hello! I had a couple of questions.

1.) When we found the solution to the inequality, what is the logical solution we found?

2.) And why is it that when we divided both sides by -3 to isolate the y variable, the sign flipped? Please provide a logical reason and an example.

Thank you!
• 1) When you solve the inequality, you have found all the values that make the inequality be true.

2) We flip the inequality when we multiply / divide by a negative value because the negative reverses the relationship between the numbers.

Consider 4 < 10. This is currently a true statement. If you divide both sides by -2 and you don't reverse the inequality, you end up with: -2 < -5, which is now a false statement. The -2 is larger than -5. This is why we need to reverse the inequality.

Hope this helps.
• what if i'm not given an equation to solve, instead just the graph? how can i be sure that the points are correct, or incorrect?
• You have to look for line points that clearly go through both x & y integer points on the graph.
• What was i suppose to learn about this? i didnt understand a single thing in this video
• When we solve equations or inequalities, we want to make sure our answers are correct. We need to make sure they make sense.

If we have 3, and our inequality is 5z - 2 > 10, we plug the 3 into the inequality to check. It comes out to be 17 > 10. Is this statement true. 3 is an answer to this inequality.
• wait, so you how did you get 15?? did you what do you multiply??