When do inequalities reverse

Imagine comparing the numbers 5 and 3. Obviously this is wrong! When you multiply both sides by a negative value you make the side that is greater have a "bigger" negative number, which actually means it is now less than the other side! This is why you must flip the sign whenever you multiply by a negative number.

You can also consider this with a number line. On a number line, 5 is to the right of 3. As an additional note—much like with division, do not multiply both sides of an inequality by a variable unless you know the sign of the variable! When we multiply or divide by a negative to solve an inequality, it's the same as multiplying or dividing by a negative to solve a regular equation!

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. 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. If the set of solutions includes any shaded area, then there are indeed an infinite number of solutions. The replacement set is the set of values that may be substituted for the variable.

To find the solution set from the replacement set, plug in each value from the replacement set and evaluate both sides of the equation. If the two sides are equal, the equation is true and thus the value is a solution. Step-by-step explanation: If the inequality states something untrue there is no solution. If an inequality would be true for all possible values, the answer is all real numbers. Begin typing your search term above and press enter to search. Press ESC to cancel.

Skip to content Home Philosophy Why do we reverse the inequality symbol? Ben Davis April 15, Why do we reverse the inequality symbol? How does the inequality sign change? Do you flip inequality sign when dividing?

We can solve inequalities using inverse operations in the same way we solve equations using inverse operations with one exception: we have to pay attention to the rules governing multiplication and division by a negative number and reciprocals, and flip the inequality sign when appropriate. Again, follow these steps to reverse the order of operations acting on the variable: Reverse addition and subtraction by subtracting and adding outside parentheses.