There is one very important exception to the rule that multiplying or dividing an inequality is the same as multiplying or dividing an equation. But to be neat it is better to have the smaller number on the left, larger on the right.

To this: Performing multiplication or division with an inequality is nearly identical to multiplying or dividing parts of traditional equations with one exception, covered below.

Our aim is to have x or whatever the variable is on its own on the left of the inequality sign:. No matter, just swap sides, but reverse the sign so it still "points at" the correct value! Because we are multiplying by a positive number, the inequalities will not change.

Combine each inequality and find the overlap i. Another thing we do is multiply or divide both sides by a value just as in Algebra - Multiplying. Solve each inequality alone.

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

If both Alex and Billy get three more coins each, Alex will still have more coins than Billy. Some things can change the direction!

Well, just look at the number line! When multiplying or dividing by a negative number, reverse the inequality.

Do not try dividing by a variable to solve an inequality unless you know the variable is always positive, or always negative. In solving multiple simultaneous inequalities using multiplication or division, the most important part is to solve each inequality separately and then combine them. The solution to the set of inequalities is the overlapping graphical area.

There are plenty of instances where you will know the sign of a variable and as a result, you can multiply or divide and know for sure whether you must flip the inequality sign. Solving Inequalities Sometimes we need to solve Inequalities like these: Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign.

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