When is inequality sign reversed

For many students, the above set of inequalities can best be understood graphically. The solution to the set of inequalities is the overlapping graphical area. Get Link. 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. However, after reading your answer it appears the short and straight answer is because of law of signs which I think is what I was looking for. The reason that the reversal for equality escapes notice is that the symbol for equality is symmetric.

Dave L. Solve Inequalities with Addition or Subtraction — Examples. View All Related Lessons. Caroline K. Multiplying and Dividing by a Negative to Solve an Inequality When we multiply or divide by a negative to solve an inequality, it's the same as multiplying or dividing by a negative to solve a regular equation! Multiplying by a Negative. Show Solution Check. Ben Ferrara.

Summary We can multiply and divide to solve inequalities just like we do with equations. Whenever we multiply or divide by a negative number, we have to flip the inequality sign. You'll need to keep track of whether you're dividing by a positive or negative number. You've reached the end. 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.