SOLUTION: Hi I am trying to solve this equation: (((x-215)*52)/x)=15 i have tried simplifying the problem: (52x-11180)/x=15 i'm unsure of the "steps" needed to solve x in this equation i

Algebra ->  Radicals -> SOLUTION: Hi I am trying to solve this equation: (((x-215)*52)/x)=15 i have tried simplifying the problem: (52x-11180)/x=15 i'm unsure of the "steps" needed to solve x in this equation i      Log On


   

Question 88518: Hi
I am trying to solve this equation: (((x-215)*52)/x)=15
i have tried simplifying the problem: (52x-11180)/x=15
i'm unsure of the "steps" needed to solve x in this equation
if you can offer any help it would be much appreciated thanks
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
%28%28x-215%29%2A52%29%2Fx=15
.
First, you can make things easier by getting rid of the denominator on the left side. You
can do this by multiplying the left side by x. But in an equation, if you multiply one side
by a quantity, you must multiply the other side by the same quantity to keep the equation
in balance. So multiply both sides of the given equation by x:
.
%28x%2A%28x-215%29%2A52%29%2Fx=15%2Ax
.
Notice that on the left side the x now in the numerator cancels with the x in the denominator
.
%28cross%28x%29%2A%28x-215%29%2A52%29%2Fcross%28x%29=15%2Ax
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and the equation becomes:
.
%28%28x-215%29%2A52%29=15%2Ax
.
Now, multiply out the left side by multiplying 52 times each quantity in the parentheses.
When you do that the equation then is:
.
52x+-+11180+=+15x
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To solve this you need to get all the terms that contain x on one side and the terms that
are just numbers on the other side. You can begin by subtracting 15x from both sides to
get rid of the 15x on the right side. This subtraction results in:
.
52x+-+15x+-11180+=+0
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The two terms containing x on the left side combine by subtraction (52x - 15x = 37x) and
the equation reduces to:
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37x+-+11180+=+0
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Next, get rid of the 11,180 on the left side by adding 11,180 to both sides. When you do
that addition the equation changes to:
.
37x+=+11180
.
Finally, solve for x by dividing both sides of this equation by 37. The equation is then:
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x+=+11180%2F37+=+302.1621622
.
So x = 302.1621622
.
Let's check by substituting that value for x in the original problem to see if the equation
is equal on both sides. The original equation you were given was:
.
%28%28x-215%29%2A52%29%2Fx=15
.
Substitute for x and the equation becomes:
.
%28%28302.1621622-215%29%2A52%29%2F302.1621622=15
.
Subtract 215 from 302.1621622 and the numerator reduces to:
.
%28%2887.1621622%29%2A52%29%2F302.1621622+=+15
.
Multiply out the numerator and the problem is then:
.
4532.432432%2F302.1621622+=+15
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Do the division on the left side and you end up with:
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15 = 15
.
That works!!! So the answer of x = 302.1621622 is correct!!!
.
Hope this helps you to understand the problem and a way to go about solving it. You were
on the right track, but just needed to get rid of the x in the denominator to simplify
the equation a little more.
.