Question 202109
You're close, but what you're actually doing is using PEMDAS in reverse. 




{{{(1/8)(7m-7)=(2/5)(4m-4)+8}}} Start with the given equation.



{{{(7/8)m-7/8=(8/5)m-8/5+8}}} Distribute.



{{{cross(40)^5((7/cross(8))m)-cross(40)^5(7/cross(8))=cross(40)^8((8/cross(5))m)-cross(40)^8(8/cross(5))+40(8)}}} Multiply EVERY term by the LCD {{{40}}} to clear any fractions.



{{{35m-35=64m-64+320}}} Multiply and simplify.



{{{35m-35=64m+256}}} Combine like terms on the right side.



{{{35m=64m+256+35}}} Add {{{35}}} to both sides.



{{{35m-64m=256+35}}} Subtract {{{64m}}} from both sides.



{{{-29m=256+35}}} Combine like terms on the left side.



{{{-29m=291}}} Combine like terms on the right side.



{{{m=(291)/(-29)}}} Divide both sides by {{{-29}}} to isolate {{{m}}}.



{{{m=-291/29}}} Reduce.



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Answer:


So the solution is {{{m=-291/29}}} which approximates to {{{m=-10.034}}}.