Question 93848
{{{(x-3)/4 - (x-1)/9 = (x-5)/6}}}



{{{36((x-3)/4 - (x-1)/9) = 36((x-5)/6)}}} Multiply both sides by the LCM 36 to eliminate the fractions


{{{9(x-3) - 4(x-1) = 6(x-5)}}} Distribute and multiply


{{{9x-27 - 4x+4 = 6x-30}}} Distribute again




{{{9x-27-4x+4-6x=-30}}} Subtract 6x from both sides



{{{9x-4x+4-6x=-30+27}}}Add 27 to both sides



{{{9x-4x-6x=-30+27-4}}}Subtract 4 from both sides



{{{-x=-30+27-4}}} Combine like terms on the left side



{{{-x=-7}}} Combine like terms on the right side



{{{x=(-7)/(-1)}}} Divide both sides by -1 to isolate x




{{{x=7}}} Reduce

      
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Answer:

So our answer is {{{x=7}}}





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Check:

 
{{{(7-3)/4 - (7-1)/9 = (7-5)/6}}} Plug in x=7


{{{4/4 - 6/9 = 2/6}}} Subtract


{{{1 - 6/9 = 2/6}}} Reduce


{{{9/9 - 6/9 = 2/6}}} Rewrite 1 as 9/9



{{{3/9 = 2/6}}} Subtract the fractions


{{{1/3 = 1/3}}} Reduce both sides. Since this equation is true, our answer is verified