Only when what you're multiplying by/dividing by is negative.
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The usual case is when you multiply or divide an inequality by a negative number.
When solving an inequality, you must revers the inequality sign when you multiply (or divide) both sides by a negative number.
The inequality sign changes direction. So 2<3 Multiply by -2 and you get -4>-6 (similarly with division).
It depends on the specific inequality. In the simplest cases, it is solved just like an equation; except that you must be careful when multiplying and dividing - if you multiply or divide both sides by a negative number, you must switch the inequality sign. For instance, a "less-than" sign would be changed to a "greater-than" sign.
When you divide both sides of an inequality by a negative number, the inequality sign flips.