you can subtract the same quantity from each side.And I want to show you what I mean and how what that looks like IB or why, for example check it out 6 is greater than four. you can add the same quantity to each side Then when you're solving you solve it just like it were if it were an equation except if you're multiplying or dividing by a negative number you need to change the direction of the inequality symbol.Because any number multiplied by 1 is that number, he is left with (in the 3x15 problem)when you divide both sides by 3, you change the 3 into a 1 and the 15 into a 5, leaving you with (1 times x 15). What are the rules for solving inequalities? Any number divided by itself is equal to 1. If we multiply or divide both sides of inequality by a single negative number, that's perfectly legal, but we must remember to reverse the direction of inequality. But, multiplying by −1 is the same as switching the signs of the numbers on both sides of the inequality, which reverses the inequality: a−b.Īlso asked, can we divide two inequalities?Įverything gets much hairier with multiplying or dividing inequalities when you consider - one or both sides could be negative. The Division and Multiplication Properties of Equality state that if two quantities are equal, when we divide or multiply both quantities by the same amount. Dividing by a negative number is the same as dividing by a positive number and then multiplying by −1. Multiply or divide the inequality by the same positive number. Thus, if you divide or multiply both sides by a positive number,the inequality sign will not change.Īlso Know, why do you switch the inequality sign when dividing by a negative? 9 Answers. Solving Inequalities Add or subtract the same number on both sides of an inequality. You only change the inequality sign if you divide or multiply both sides by a negative number. Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign.Ĭonsequently, what happens to inequalities when you divide? To solve, you need to get all the x -es on the same side of the inequality. For example, consider the following problem: 3x + 6 > 6x + 12. There is one very important exception to the rule that multiplying or dividing an inequality is the same as multiplying or dividing an equation. The main situation where youll need to flip the inequality sign is when you multiply or divide both sides of an inequality by a negative number. When solving each Two Step Inequality you will have to either add or subtract first and then multiply or divide second to solve the inequality.
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