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In which case do you need to reverse the inequality sign when solving an inequality?
when adding or subtracting a negative number
when multiplying or dividing by a negative number
when there is a line under the equality symbol
where there is no line under the equality symbol

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miriyu
when multiplying or dividing by a negative number. this changes the sign because, when you divide/multiply by a negative number, you're changing the sign on BOTH sides of the inequality. what was originally negative would become positive, and vice versa. because of that, you have to flip the sign.

if you DON'T flip the sign, you usually end up with a "backwards" inequality, such as 4 < x, but the rules tell you to write "4 is less than x" as "x is greater than 4" (x > 4) so you end up rearranging the sign anyways--it's just easier to do it as you go.

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