Question 93529
In equation form you are given:
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{{{-12>=24x}}}
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You can pretty much work these using the same procedures that you would to solve an equation.
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However, there is an exception. This exception is that in solving for x if you ever have to
MULTIPLY or DIVIDE both sides by a NEGATIVE quantity, then you also have to reverse the 
direction of the inequality sign.
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Let's work this problem. 
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If this were an equation, you would solve for x by dividing both sides by 24 because 24
is the multiplier of x. So let's divide both sides by +24 to get:
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{{{-12/24>=(24x)/24}}}
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Notice that on the left side if you divide both the numerator and denominator by 12 you are
left with {{{-1/2}}} and on the right side the 24 in the numerator cancels with the 24
in the denominator. Therefore, all you are left with is:
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{{{-1/2>=x}}}
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That's the answer. Now, what does it mean? It says that {{{-1/2}}} is greater than or equal
to x. (Remember that the inequality sign always points to the smaller quantity.)
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This also means the same as x is less than or equal to {{{-1/2}}}. For the purposes of
graphing this answer, you can draw a number line. Then put a dot at the point {{{-1/2}}}.
x can have that value. x can also be less than that number. That means that x can be any 
value to the left of the point at {{{-1/2}}}. So you make the number line to the left of the
point {{{-1/2}}} a very heavy line to indicate that x can be on that part of the line.  
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Hopefully this makes some sense to you.  In solving this problem we didn't have to multiply
or divide both sides by a negative number, so we didn't need to use the rule about 
changing the direction of the inequality sign.  It just stayed the same direction 
throughout all our work.  
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Remember the goal is to solve inequalities for +x. If you have a problem that you can solve
for -x, then do so. But at the very end of the problem you will need to multiply the -x by
-1 to change it to +x. And when you multiply one side by -1 you must also multiply the
other side by -1 ... and that means that you also need to reverse the direction of the 
inequality sign because you multiplied both sides by a minus number.