When do inequality signs flip

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. One very important implication of this rule is: You cannot divide by an unknown i. 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.

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. Now, you need to rewrite this expression as a compound inequality. The output of an absolute value expression is always positive, but the " x " inside the absolute value signs might be negative, so we need to consider the case when x is negative.

That gives us our two inequalities or our "compound inequality". We can easily solve both of them. These kinds of problems take some practice, so don't worry if you aren't getting it at first! Keep at it and it will eventually become second nature. You also often need to flip the inequality sign when solving inequalities with absolute values. How to Divide Negative Fractions.

How to Solve Double Inequalities. Standard Form of a Linear Equation. How to Solve Inequalities With Fractions. How to Divide Negative Numbers. How to Determine Linear Equations. How to Do Math Problems in Algebra 1. How to Calculate the Equation of a Line.

How to Solve Absolute Value Inequalities. How to Find the Domain of a Function Defined by an How to Compare Negative Fractions. How to Solve for a Variable.