What are the similarities and differences in solving equations and inequalities?

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Question

What are the similarities and differences in solving equations and inequalities? 

PLZ HELP

anonymous · Answer

They obey the same rules with the exception of applying 'decreasing' functions to both sides (which inverts the inequality). By that, I mean:

Say we have $a<b$, then, the function $-x$ is decreasing for all $x$. Hence, if we apply it to both sides, we get $a<b\implies -a>-b$.

anonymous · Answer

What LolWolf said, everything is the same mechanics when transferring (adding, subtracting, multiplying and dividing) and bringing to the other side. But if the sign changes of the other side, you must switch the inequality around.

anonymous · Answer

Additionally, say you take the reciprocal of both sides, then the same case applies.
If
$$
a<b
$$Then:
$$
\frac{1}{a}>\frac{1}{b}
$$If the sign of $a, b$ is the same.