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What is the answer?

by Lucy
(Chicago)











































What is X in the following equation:

5/x+3 = 1/x plus 1/2x

in addition to the answer what is the step by step process to get the answer?

Comments for What is the answer?

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Dec 09, 2010
Equation Solution
by: Staff

The question:


by Lucy
(Chicago)


What is X in the following equation:

5/x+3 = 1/x plus 1/2x

in addition to the answer what is the step by step process to get the answer?



The answer:

You didn’t use parentheses in your equation, but I think this is what you mean:

5/(x+3) = 1/x + 1/2x


There is more than one approach you can use, but I’m going to start by eliminating the denominator on the left hand side of the equation.

To accomplish this, I will multiply both sides of the equation by (x+3).

(x+3) * [5/(x+3)] = (x+3) * [1/x + 1/2x]

[5*(x+3)/(x+3)] = [(x+3) * (1/x) + (x+3) * (1/2x)]

5*[(x+3)/(x+3)] = [(x+3) * (1/x) + (x+3) * (1/2x)]

5*1 = [1*(x+3)/x + 1*(x+3)/2x)]

5 = (x+3)/x + (x+3)/(2x)


Next, I am going to eliminate the x in the denominators of the two fractions on the right hand side of the equation.

To accomplish this, I will multiply both sides of the equation by (2x).

5 = (x+3)/x + (x+3)/(2x)

2x*5 = 2x*[(x+3)/x + (x+3)/(2x)]

2*5*x = [2x*(x+3)/x + 2x*(x+3)/(2x)]

10*x = (x+3)*(2x/x) + (x+3)* (2x/2x)

10*x = (x+3)*2*1 + (x+3)*1

10x = (x+3)*2 + (x+3)*1

10x = (2*x+2*3) + (x+3)

10x = (2x+6) + (x+3)

10x = 2x+6+x+3

10x = 2x+x+6+3

10x = 3x+9


Next, I’m going to eliminate the 3x from the right side of the equation by subtracting 3x from each side of the equation.

10x – 3x = 3x – 3x + 9

7x = 0 + 9

7x = 9


The last step: divide each side of the equation by 7

7x/7 = 9/7

x*(7/7) = 9/7

x*1 = 9/7

x = 9/7


The final answer is: x = 9/7 (or, x = 1.2857)


You should also check the solution by substituting 9/7 for x in the original equation.

When you do, you should get the following result:

1.66666... = 1.66666...



Thanks for writing.


Staff
www.solving-math-problems.com


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