When do i flip an inequality

Just remember to multiply or divide both sides by the same quantity, then simplify! Here Patrick JMT has a good video explaining how to go about solving a few inequalities using division. We can multiply and divide to solve inequalities just like we do with equations. But, there is one catch. Solve Inequalities with Negative Multiplication or Division — Examples - Expii Solving an inequality with multiplication or division of a negative number flips the inequality symbol.

Pre-Algebra One-Step Inequalities. Explanations 3. Tommy San Miguel. Solving Inequalities: Multiplication by a Negative Number: Sometimes, it is necessary to multiply an inequality by a negative number in order to solve the inequality. We'll try to move everything else to the other side. Here's why: Imagine comparing the numbers 5 and 3. Performing multiplication or division with an inequality is nearly identical to multiplying or dividing parts of traditional equations with one exception, covered below.

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. 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. 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. An inequality with lots of negatives and absolute values. When do you flip the inequality sign? No fear! There are a couple of occasions when you flip the inequality, and we'll go through them below. Flip the inequality sign when you multiply or divide both sides of an inequality by a negative number.

The main situation where you'll need to flip the inequality sign is when you multiply or divide both sides of an inequality by a negative number. To solve, you need to get all the x -es on the same side of the inequality. Now isolate the x on the left side by moving the constant, 6, to the other side of the inequality. To do this, subtract 6 from both sides.