How do you solve #(x+1)/3 = (2x-1)/4#?

2 Answers
Jim G.
Jun 21, 2018

#x=7/2#

Explanation:

#"multiply both sides by the lowest common multiple of"#
#"3 and 4 that is 12"#

#cancel(12)^4xx(x+1)/cancel(3)^1=cancel(12)^3xx(2x-1)/cancel(4)^1#

#4(x+1)=3(2x-1)larrcolor(blue)"distribute"#

#4x+4=6x-3#

#"subtract "4x" from both sides"#

#4=2x-3#

#"add 3 to both sides and divide by 2"#

#7=2xrArrx=7/2#

#color(blue)"As a check"#

#"left "=(7/2+2/2)/3=(9/2)/3=9/6=3/2#

#"right "=(14/2-2/2)/4=6/4=3/2#

#x=7/2" is the solution"#

KillerBunny
Jun 21, 2018

#x = 7/2#

Explanation:

Multiply both sides by #12#:

#cancel(12)^4\frac{x+1}{cancel(3)} = \frac{2x-1}{cancel(4)}cancel(12)^3#

So, the equation becomes

#4(x+1)=3(2x-1)#

Expand both sides to get

#4x+4 = 6x-3#

Subtract #6x# to both sides:

#-2x+4=-3#

Subtract #4# from both sides:

#-2x = -7#

Divide both sides by #-2#:

#x = 7/2#

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