Why does inequality signs changed

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. Renfro Dave L. Renfro Bill Dubuque Bill Dubuque k 36 36 gold badges silver badges bronze badges. At its essence it is a law of an ordered field. Mark Mark 5, 28 28 silver badges 29 29 bronze badges. Larry B. Ali Ali 11 1 1 bronze badge. Upcoming Events. Featured on Meta. Now live: A fully responsive profile. The unofficial elections nomination post. Linked However, you must always ask yourself whether you know for sure the sign of the variable before dividing or multiplying when dealing with an inequality.

Just as it is possible to solve two simultaneous equations, so it is possible to solve two inequalities or three, or four, etc.

In solving multiple simultaneous inequalities using multiplication or division, the most important part is to solve each inequality separately and then combine them.

Michael Kelley. All rights reserved including the right of reproduction in whole or in part in any form. You can purchase this book at Amazon. Algebra Linear Inequalities Equations vs. Critical Point When you solved equations, you were advised to do the same things to both sides of the equal sign.

You've Got Problems Problem 2: Solve the inequality 2 w - 6 See also:. Algebra: Graphing Solutions. To solve, you need to get all the x-es on the same side of the inequality. There is one very important exception to the rule that multiplying or dividing an inequality is the same as multiplying or dividing an equation.

Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign. 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.