Question 208439: 20-4 over 5x is greater then or equal to 16?
greater then=> (if i have it wrong, its less then)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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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