How do you solve #(X+3)/(2) -(X-4)/(7) = 1#?

2 Answers
Jan 19, 2017

Answer:

See the entire solution process below.

Explanation:

First, multiply each side of the equation by the lowest common denominator for both fractions, #color(red)(14)#, to eliminate the fractions while keeping the equation balanced:

#color(red)(14)((X + 3)/2 - (X - 4)/7) = color(red)(14) xx 1#

#(color(red)(14) xx (X + 3)/2) - (color(red)(14) xx (X - 4)/7) = 14#

#(cancel(color(red)(14))7 xx ((X + 3))/color(red)(cancel(color(black)(2)))) - (cancel(color(red)(14))2 xx ((X - 4))/color(red)(cancel(color(black)(7)))) = 14#

#7(X + 3) - 2(X - 4) = 14#

#7X + 21 - 2X + 8 = 14#

#5X + 29 = 14#

#5X + 29 - color(red)(29) = 14 - color(red)(29)#

#5X + 0 = -15#

#5X = -15#

#(5X)/color(red)(5) = -15/color(red)(5)#

#(color(red)(cancel(color(black)(5)))X)/cancel(color(red)(5)) = -3#

#X = -3#

Jan 20, 2017

Answer:

#x=-3#

Explanation:

Making the denominators all the same.

#" "color(green)([ (x+3)/2color(red)(xx1)]" " -" "[(x-4)/7color(red)(xx1)]=[1color(red)(xx1)]#

#" "color(green)([ (x+3)/2color(red)(xx7/7)]color(white)(..) -color(white)(.)[(x-4)/7color(red)(xx2/2)]=[1color(red)(xx14/14)]#

#" "color(green)([ (7x+21)/14]" "color(white)(.) -color(white)(...)[(2x-8)/14]" "=" "[14/14]#

Multiply everything by 14

#" "color(green)(7xcolor(red)(+21) -2xcolor(red)(+8)=14)#

#" "color(green)(7x-2xcolor(red)(+21+8)=14 )larr# Regrouped

#" "5x+29=14#

Subtract 29 from both sides

#" "5x=-15#

Divide both sides by 5

#" "x=-3#