How do you solve #x/4 - 2/3+(3x)/2 = 3/4 -(2x)/3#?

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Answer 1 · 2016-10-08T14:36:52

#x=17/29#

Least common denominator on both terms:

#\frac{3x-8+18x}{12} = \frac{9-8x}{12}#

As you can see, the two denominators are equal. The only possibility for an equivalence like

#a/b = c/b# is that #a=c#, so you can only consider the numerators:

#3x-8+18x=9-8x#

Summing the similar terms:

#21x-8=9-8x#

Bring all the #x# terms on the left and all the constants to the right:

#21x+8x=9+8#

Sum again:

#29x=17#

Solve for #x#:

#x=17/29#