Question 208439
you manipulate inequalities much the same way you manipulate equalities.
the only real difference is that if you multiply both sides of an inequality by -1 then you reverse the inequality.
example:
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equality:
a = b
multiply both sides by -1 to get:
-a = -b
the signs are reversed and the equality is preserved.
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inequality:
a > b
multiply both sides by -1 to get:
-a < -b
the signs are reversed and the inequality is reversed.  where it said > now it says <.
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your equation looks like this:
(20-4)/5x >= 16
as far as i can tell.
to solve this you do the following:
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multiply both sides by x to bring the x over to the right side of the equation and remove it from the denominator.
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you get:
(20-4)/5 >= 16 * x
which becomes:
16/5 >= 16x
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divide both sides by 16 to get:
16/(16*5) >= x
this becomes:
1/5 >= x
to get x over to the left side of this equation you have to subtract x from both sides of this equation and to get 1/5 over to the right side of this equation you have to subtract 1/5 from both sides of this equation.
you get:
-x >= - (1/5)
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here's where the reversal of signs comes in.
if you multiply both sides of this equation by (-1) you get:
x <= (1/5)
note the inequality was reversed.
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the answer to this question is that if x <= 1/5, then the original equation of 16/5x >= 16 holds true, assuming i interpreted the original equation correctly.
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if x = 1/5 = .2, this equation becomes 16/1 >= 16 which is true.
if x = .3, this equation becomes 16/1.5 >= 16 which is false.
if x = .1, this equation becomes 16/.5 >= 16 which is true.
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answer is x <= (1/5)
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