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

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Answer 1 · 2017-07-22T14:02:43

#x = -7#

#4(x - 3) = 2(3x + 1)#
#rArr 2(x - 3) = 3x + 1#
#rArr 2x - 6 = 3x + 1#
#rArr -6 - 1 = 3x - 2x#

#therefore x = -7#

Answer 2 · 2017-07-22T14:09:15

#x=-7#

#color(green)((x-3)/2color(red)(xx1)" "=" "(3x+1)/4)#

#color(green)((x-3)/2color(red)(xx2/2)" "=" "(3x+1)/4)#

#color(green)((color(red)(2)(x-3))/(2color(red)(xx2))" "=" "(3x+1)/4)#

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

Two ways of looking at the next step

Concept 1: multiply both sides by 4

Concept 2: As the denominators are the same then we only need to consider the numerators.

#2x-6=3x+1#

Subtract #2x# from both sides

#-6=x+1#

Subtract 1 from both sides

#-7=x#

#x=-7#
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Check:

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

#(-7-3)/2=(-21+1)/4#

#" "-5" "=" "-5#