by Lucy
(Chicago)

What is X in the following equation:

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

 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