How do you solve #\frac{x-10}{5}+\frac{x-8}{6}+\frac{x-5}{10}=\frac{x-11}{3}-\frac{5}{2}#?

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Answer 1 · 2016-10-22T17:20:18

#x=-35/2#

#(x-10)/5+(x-8)/6+(x-5)/10 = (x-11)/3 - 5/2#

The least common multiple of all of the denominators is #30#, so multiply the equation through by #30# to get:

#6(x-10)+5(x-8)+3(x-5)=10(x-11)-15(5)#

Multiply out the brackets to get:

#6x-60+5x-40+3x-15=10x-110-75#

Collect terms and combine to get:

#14x-115 = 10x-185#

Add #115-10x# to both sides to get:

#4x = -70#

Divide both sides by #4# to get:

#x = -70/4 = -35/2#