Math and Arithmetic
Algebra
Numbers

# What happens to the inequality when it is multiplied by a negative number?

345 ###### 2010-12-01 05:09:26

The inequality is "flipped" when multiplied by a negative number. For example, if x > y and a is a negative number, then ax < ay.

🦃
0
🤨
0
😮
0
😂
0

## Related Questions  When an inequality is multiplied or divided by a negative number the inequality sign is reversed.Example : -x -14 When one side of the inequality is divided or multiplied by a negative number. When an Inequality expression is multiplied (or divided) by a negative number then the Inequality sign is reversed. Example : -9x &lt; 18 : -x &lt; 2 : x &gt; -2........as both sides have been multiplied by -1. The direction of the inequality is reversed. Note that the if the inequality included "or equals" before, then it will after. 4 &lt; 5 multiplied by -1 gives -4 &gt; -5 5 &gt;= 4 multiplied by -1 gives -5 &lt;= -4 When a side is multiplied or divided by a negative number. When the two sides of the inequality are multiplied or divided by a negative number or term or expression. The inequality symbol doesn't change direction in this case.Note that that is the same as adding a positive number.Note also that if you MULTIPLY or DIVIDE by a negative number, then you need to change the direction of the inequality symbol. In the case of an inequality, if you mulitply by a negative number, you have to reverse the direction of the inequality. E.g.: -x &lt; 10 becomes: x &gt; -10 (Here, I multiplied by -1, and simultaneously reversed the direction of the inequality.) If two sides of an inequality are multiplied (or divided) by a negative number, you have to invert the sign. For example, a "less-than" sign becomes a "greater-than" sign. Nothing, you proceed as if the &lt; or &gt; was an =. If you're multiplying or dividing both sides by a negative, you flip the sign. e.g. &lt; would go to &gt; If an inequality is multiplied or divided by a negative number then the inequality sign is switched. For example, -2x &gt; 4 then -2x/-2 &gt; 4/-2 then x &lt; -2. No No. Positive number multiplied by a negative number gives a negative number.  A negative number multiplied by another negative number equals a positive number. For example, -5 &middot; -5 = positive 25. The negative number multiplied by one, the answer stays the same. for example -52 x 1 = -52 No, you only flip the inequality sign if you are dividing by a negative number on both sides of the inequality The rules for dividing negative numbers is the same as multiplying them. A negative number multiplied/divided by a negative number is positive and a negative number multiplied/divided by a positive number is negative. The inequality sign changes direction. So 2&lt;3 Multiply by -2 and you get -4&gt;-6 (similarly with division). 40 (a negative number multiplied by a negative number is always a positive number.) no. a negative multiplied by a negative is a positive. A negative number multiplied by a negative number will result in a positive answer. Multiplying anything non-zero by a negative number changes the sign. A positive number multiplied by a negative number becomes negative. A negative number multiplied by a negative number becomes positive. The answer of a negative number multiplied by (or divided by) a positive number will be a negative number. A negative number multiplied by a negative yields a positive answer.

###### Math and ArithmeticAlgebraInternational Government Copyright © 2020 Multiply Media, LLC. All Rights Reserved. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply.