How do you solve #\frac { 4x } { 3} + \frac { x + 1} { 2} = \frac { 7} { 3}#?

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Answer 1 · 2017-07-17T05:03:05

#x=1#

#(4x)/3+(x+1)/2=7/3#

We multiply all terms by #6#, which is the LCM of the denominators, so as to convert the fractions into whole numbers.

#(6xx(4x)/3)+(6xx(x+1)/2)=6xx7/3#

#(2cancel6xx(4x)/(1cancel3))+(3cancel6xx(x+1)/(1cancel2))=2cancel6xx7/(1cancel3)#

#(2xx4x)+(3xx(x+1))=2xx7#

#8x+3x+3=14#

#11x+3=14#

Subtract #3# from each side.

#11x+3-3=14-3#

#11x=11#

Divide both sides by #11#.

#(11x)/11=11/11#

#(1cancel11x)/(1cancel11)=(1cancel11)/(1cancel11)#

#x=1#