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Algebra (all content)

Course: Algebra (all content)>Unit 6

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.

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• How do you exactly test a point?
• Substitute the x and y values of your point into the inequality. If the statement is true, that point is part of the solution. If the statement is false the point is not in the solution.
• how do you know you have the right answer and if you graphed it correctly?
• Watch more videos. Sal usually shows multiple ways of solving problems and checking your answers.
• 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.
• 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.
• 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.
• What do you do if an inequality is (example) x>1 or y>1 with no slope? Which ones go which way?
• y>1 has a slope of 0 and is horizontal (it is parallel to the x-axis). That means you should draw a dotted line at y=1.
x>1 has no slope and is vertical (parallel to the y-axis). That means you draw a dotted line at x=1.
• Do you only switch the inequality signs when two negatives are being divided?
(1 vote)
• Well, you are supposed to do that in this case, but it doesn't include everything. When multiplying or dividing in inequalities and a negative number is somewhere, know this:
1. If you are multiplying, and the number that is multiplying (say you have 4 > -7/3 x; the number that I'm talking about would be the reciprocal of x's coefficient [-3/7]) is negative, flip the sign.
2. If the number that is multiplying is positive, don't flip the sign, even if the number multiplied (in the equation above, the number I'm talking about would be 4) is negative.
3. If you are dividing, and the divisor is negative, flip the sign.
4. If the divisor is positive, don't flip the sign, even if the dividend is negative.
• At , Sal said that is not true that 0 is greater than or equal to 25! Wouldn't he flip the inequality sign?