Question 112969
{{{(7/5)(10m-1)<(2/3)(6m+5)}}} Start with the given inequality




{{{(15)((7/5)(10m-1))<(15)((2/3)(6m+5))}}} Multiply both sides by the LCM of 15. This will eliminate the fractions  (note: if you need help with finding the LCM, check out this <a href=http://www.algebra.com/algebra/homework/divisibility/least-common-multiple.solver>solver</a>)




{{{21(10m-1)<10(6m+5)}}} Distribute and multiply the LCM to each side




{{{210m-21<60m+50}}} Distribute



{{{210m<60m+50+21}}}Add 21 to both sides



{{{210m-60m<50+21}}} Subtract 60m from both sides



{{{150m<50+21}}} Combine like terms on the left side



{{{150m<71}}} Combine like terms on the right side



{{{m<(71)/(150)}}} Divide both sides by 150 to isolate m 




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Answer:

So our answer is {{{m<71/150}}}  (which is approximately {{{m<0.473333333333333}}} in decimal form)