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dividing inequalities by negative number
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Question:Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations?
Answers:Consider the statement 4 < 7, which is true. If you multiply both sides by 1 but you did not change the direction of the sign you would have 4 < 7, which is a false statement. Therefore, the direction must be changed, as well: 4 > 7. Yes, this holds true for equations, as well. 2  3x > 5 3x > 3 (and now divide by 3) x < 1
Answers:Consider the statement 4 < 7, which is true. If you multiply both sides by 1 but you did not change the direction of the sign you would have 4 < 7, which is a false statement. Therefore, the direction must be changed, as well: 4 > 7. Yes, this holds true for equations, as well. 2  3x > 5 3x > 3 (and now divide by 3) x < 1
Question:1. A) Why does the inequality sign change when both sides are multiplied or divided by a negative number?
B) Does this happen with equations? Why or why not?
Write an inequality for your classmates to solve. In your inequality, use both the multiplication and addition properties of inequalities.
Answers:No need to "memorize" this. I always suggest people prove it for themselves. First, wriite down an inequality that you know is true, and do whatever you want to it to see how you would have to change the inequality sign for each test. For instance, 2 is less than 3, so in terms of an inequality we can write 2 < 3 What happens if you multiply both sides by a negative number, say 5? 2*(5) < 3*(5) 10 < 15 but that is not true, so you should write: 10 > 15, see how the sign flipped? This is not so much a question of why, as just learning a set of rules. What if you divide the statement 2 < 3, by 5? 2/5 < 3/5 ? Sure, that is also true. What about dividing by 5? 2/5 < 3/5? No, 3/5 is more negative than 2/5, so we would have to write 2/5 > 3/5 for the inequalilty to be true. So, we conclude that multiplying or dividing by a negative number forces a flip of the inequality sign to have consistent math. (B) for equations, there is no inequality sign to flip, an equation is an 'equality' (i.e. has an equal sign, so this cannot happen for equations). Asa a final note, inequalities do not need to just be wtih numbers, they can involve variables like x. Make sense?
Answers:No need to "memorize" this. I always suggest people prove it for themselves. First, wriite down an inequality that you know is true, and do whatever you want to it to see how you would have to change the inequality sign for each test. For instance, 2 is less than 3, so in terms of an inequality we can write 2 < 3 What happens if you multiply both sides by a negative number, say 5? 2*(5) < 3*(5) 10 < 15 but that is not true, so you should write: 10 > 15, see how the sign flipped? This is not so much a question of why, as just learning a set of rules. What if you divide the statement 2 < 3, by 5? 2/5 < 3/5 ? Sure, that is also true. What about dividing by 5? 2/5 < 3/5? No, 3/5 is more negative than 2/5, so we would have to write 2/5 > 3/5 for the inequalilty to be true. So, we conclude that multiplying or dividing by a negative number forces a flip of the inequality sign to have consistent math. (B) for equations, there is no inequality sign to flip, an equation is an 'equality' (i.e. has an equal sign, so this cannot happen for equations). Asa a final note, inequalities do not need to just be wtih numbers, they can involve variables like x. Make sense?
Question:Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Why or Why not?
Write an inequality for your classmates to solve. In your inequality, use both the multiplication and addition properties of inequalities.
Answers:Think about it like this: the larger the number is when positive, the smaller the number is when negative because it's far away from zero, but far in a negative direction is smaller. Also, think about it like this: 2x + 8 > 0 2x > 8 x ? 4 What if instead, you add 2x to both sides instead of dividing by 2 at the end? 2x + 8 > 0 8 > 2x 4 > x
Answers:Think about it like this: the larger the number is when positive, the smaller the number is when negative because it's far away from zero, but far in a negative direction is smaller. Also, think about it like this: 2x + 8 > 0 2x > 8 x ? 4 What if instead, you add 2x to both sides instead of dividing by 2 at the end? 2x + 8 > 0 8 > 2x 4 > x
Question:Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Why or why not? Write an inequality for your classmates to solve. In your inequality, use both the multiplication and addition properties of inequalities.
Answers:Simple illustration: Clearly 5 >1 but 5 < 1 Again, 2 > 3, but 2 < 3 Another way of explaining this is that for two positive numbers, the one further from 0 is greater than (i.e. to the right of) the other, but for two negative numbers the one further from 0 is less than (i.e. to the left of) the other. More abstract answer: If x > y, then for positive p, px > py Add px  py to both sides: py >  px which is equivalent to px < py As for equations, well ... have you thought about this at all for yourself, or do you want someone to supply you with a completed homework answer without any input from you? What happens if you reverse "="? It's still "=", isn't it. You can figure an example.
Answers:Simple illustration: Clearly 5 >1 but 5 < 1 Again, 2 > 3, but 2 < 3 Another way of explaining this is that for two positive numbers, the one further from 0 is greater than (i.e. to the right of) the other, but for two negative numbers the one further from 0 is less than (i.e. to the left of) the other. More abstract answer: If x > y, then for positive p, px > py Add px  py to both sides: py >  px which is equivalent to px < py As for equations, well ... have you thought about this at all for yourself, or do you want someone to supply you with a completed homework answer without any input from you? What happens if you reverse "="? It's still "=", isn't it. You can figure an example.
From Youtube
Math Fractions & Equations : How to Divide Inequalities :When dividing inequalities, treat the equation like any other standard equation. Flip the inequality sign when dividing an inequality by a negative number with help from a math author and teacher in this free video on math lessons. Expert: Brian Leaf Contact: www.brianleaf.com Bio: Brian Leaf, MA, is the author of McGrawHill's Top 50 Skills for SAT/ACT Success series and has instructed SAT, ACT, GED and SSAT preparation to thousands of students. Filmmaker: David Pakman
Dividing Negatives :Simplifying expressions with negative numbers and division.