document.write( "Question 176215: Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Why or why not? Write an inequality and use both multiplication and addition properties of inequalities. \n" ); document.write( "

Algebra.Com's Answer #131305 by solver91311(24713) $\"\"$ $\"About$

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\n" ); document.write( "Think about the statement $\"3+%3E+2\"$ . This statement is clearly true. But if you multiply both sides by $\"-1\"$ , you get $\"-3+%3E+-2\"$ which is no longer a true statement until you also reverse the sense of the inequality, namely $\"-3+%3C+-2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Another way to think about it is to consider the statement $\"a+%3E+b\"$ . This statement is true if and only if $\"a\"$ is to the left of $\"b\"$ on the number line. But if you multiply by $\"-1\"$ , you now have $\"-a\"$ to the right of $\"-b\"$ on the number line and therefore $\"-a+%3C+-b\"$ .\r
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\n" ); document.write( "\n" ); document.write( "As for equations, the only way you can change an equal sign is to make it a NOT equal sign. Multiplying both sides of an equation by a negative number doesn't make the two sides unequal, so the equal sign does not change.\r
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\n" ); document.write( "\n" ); document.write( "You can make up your own inequality as an example. \n" ); document.write( "

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