Yes you have to flip the sign.
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Change the direction of the inequality.
Always.
You divide as normal BUT you change the direction of the inequality symbol, so that < becomes > and conversely.
When an inequality is multiplied or divided by a negative number the inequality sign is reversed.Example : -x < 7 ......after multiplying by (say) -2 this becomes 2x > -14
When an Inequality expression is multiplied (or divided) by a negative number then the Inequality sign is reversed. Example : -9x < 18 : -x < 2 : x > -2........as both sides have been multiplied by -1.