Question 225860
Solve: {{{(10)/(a-7) = (-4)/(a+4)}}}


Step 1.  Multiply by (a-7)(a+4) to both sides of the equation to get rid of denominators.


{{{(10)(a-7)(a+4)/(a-7) = (-4)(a-7)(a+4)/(a+4)}}}


{{{10(a+4)=-4(a-7)}}}


{{{10a+40=-4a+28}}}


Step 2.  Add 4a-40 to both sides of the equation to get numbers on one side and variables on the other side.


{{{10a+40+4a-40=-4a+28+4a-40}}}


{{{14a=-12}}}


Step 3.  Divide by 14 to both sides of the equation to get a.



{{{14a/14=-12/14}}}


{{{a=-12/14}}}


{{{a=-6/7}}}


Step 4.  Check solution with original equation {{{(10)/(a-7) = (-4)/(a+4)}}} to see if it leads to a true statement.


{{{(10)/(-6/7-7) = (-4)/(-6/7+4)}}}


{{{10/((-6-49)/7)=(-4)/((-6+28)/7)}}}


 
{{{10/(-55/7)=(-4)/(22/7)}}} 


{{{-70/55=-28/22}}}


{{{-14/11=-14/11}}} which is a true statement.


Step 5.  ANSWER is {{{a=-6/7}}}



I hope the above steps were helpful.


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Respectfully,
Dr J

http://www.FreedomUniversity.TV