Question 161510
{{{1/10 - (x-4)/x = 1/x + 3/20}}} Start with the given equation.



{{{(20x)(1/cross(10)) - (20x)((x-4)/cross(x)) = (20x)(1/cross(x)) + (20x)(3/cross(20))}}} Multiply <b>every</b> term by the LCD {{{20x}}} to clear the fractions.




{{{2x - 20(x-4) = 20 + 3x}}} Multiply and simplify



{{{2x-20x+80=20+3x}}} Distribute.



{{{-18x+80=20+3x}}} Combine like terms on the left side.



{{{-18x=20+3x-80}}} Subtract {{{80}}} from both sides.



{{{-18x-3x=20-80}}} Subtract {{{3x}}} from both sides.



{{{-21x=20-80}}} Combine like terms on the left side.



{{{-21x=-60}}} Combine like terms on the right side.



{{{x=(-60)/(-21)}}} Divide both sides by {{{-21}}} to isolate {{{x}}}.



{{{x=20/7}}} Reduce.



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Answer:


So the answer is {{{x=20/7}}} which approximates to {{{x=2.857}}}.