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How do you do inequalities

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Adam H. | Honest, Reliable, College Student Tutoring Various SubjectsHonest, Reliable, College Student Tutori...

Since I am not sure as to whether you are referring to solving basic inequalities or solving inequalities to graph, I will give you the overview of the first category first.

You solve an inequality in the same fashion that is used to solve a regular equation with a variable such as 5x-2=8.  The only difference is that instead of there being an equal sign, you will have a greater than(>), less than (<), greater than or equal to (>), or less than or equal to (<) sign in it's place.  

The objective is find out what value of the variable will make the statement true.

Using the example that I mentioned above, if your problem was 


You would be looking for the value of x that would make the statement (5x-2) is greater than 8 true.  This side that the symbol opens up to is always the side that is greater.

You would treat the problem like you normally would when solving for x and add 2 to both sides


You would then divide both sides of the equation by 5 in order to isolate x


So in this case x is any number that is greater than two.  This makes sense because 5 times a number greater than 2, say 5*3=15, for example, you would be able to plug that in to your inequality and get 13>8, which would make the statement true.  Using 2, however does not make the statement true.  5*2=10.  When you plug that back into your inequality, you wind up with 8>8, which is not a true statement.  If you had, say, a greater than or equal sign (>), x would be any number greater than 2, but also the number 2 its self making the use of 2 for x a true statement.

Also, note that whenever you multiply or divide an inequality by a negative number, you must flip the inequality symbol. If your original equation had been


You would follow the same rules, adding 2 to both sides, and then dividing both sides by the coefficient of x to isolate it.  You would have to be sure to flip the sign around, though, because the coefficient of x is negative.  



This would mean that x must be any number less than 2 to make this inequality true.

I hope that this helps.  Please let me know if you need help with anything else or are looking for something a bit more specific such as solving inequalities of two variable for graphing purposes.