When do i flip inequalities

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Create a free Team What is Teams? Learn more. Why do we reverse inequality sign when dividing by negative number? Ask Question. Asked 9 years, 10 months ago. Active 1 year, 2 months ago. Viewed k times. Sniper Clown Sniper Clown 1, 2 2 gold badges 17 17 silver badges 34 34 bronze badges.

Instead I give link on Inequalities by Lawrence Spector which answers it in thorough detail introducing theorem of inequalities and their proofs. Add a comment. Active Oldest Votes. Seeing why 1 is true is not too hard. The other cases can be handled similarly. But, perhaps a bit of rigor is needed here. David Mitra David Mitra Either it is circular or so incomplete to be of little help. Alas, the OP doesn't know what he's missing by accepting it. Perhaps you may wish to do him a favor by improving the answer.

Will Fisher Will Fisher 5, 1 1 gold badge 14 14 silver badges 34 34 bronze badges. You can take reciprocals using only multiplication and division In algebra, there are rules for what you can do to an equation or inequality to make sure it stays true. Upcoming Events. Featured on Meta. Now live: A fully responsive profile. The unofficial elections nomination post. Linked 3. Related Hot Network Questions.

Question feed. Mathematics Stack Exchange works best with JavaScript enabled. Accept all cookies Customize settings. If both sides of an inequality are multiplied or divided by the same positive value, the resulting inequality is true.

If both sides are multiplied or divided by the same negative value, the direction of the inequality changes. Pick a value greater than , such as 2, to check in the inequality. Solve for x. Divide both sides by 3 to isolate the variable. Check your solution by first checking the end point 4, and then checking another solution for the inequality.

Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. There are five systems or types of social inequality: wealth inequality, treatment and responsibility inequality, political inequality, life inequality, and membership inequality. Political inequality is the difference brought about by the ability to access governmental resources which therefore have no civic equality. First of all, we can add inequalities with the same direction.

In other words, with the inequalities pointing in the same direction. So if a is greater than b and c is greater than d, then we can just add them together. For example, 5 is greater than 2 and 11 is greater than 8, those are two true inequalities. Rule 1. Adding or subtracting the same quantity from both sides of an inequality leaves the inequality symbol unchanged. Rule 2. Multiplying or dividing both sides by a positive number leaves the inequality symbol unchanged.