How do you solve #\frac { 1} { 4} ( x + 6) = \frac { 1} { 6} ( x + 8)#?

1 Answer
Mar 7, 2018

Answer:

The solution is #x=-2#.

Explanation:

Multiply both sides by #4# and then #3# to cancel out the fractions. Then, use the distributive property to get like terms and isolate #x#:

#1/4(x+6)=1/6(x+8)#

#color(blue)(4*)1/4(x+6)=color(blue)(4*)1/6(x+8)#

#color(red)cancelcolor(black)(color(blue)(4*)1/4)(x+6)=color(blue)(4*)1/6(x+8)#

#x+6=color(blue)4/6(x+8)#

#x+6=color(blue)2/3(x+8)#

#color(blue)(3*)(x+6)=color(blue)(3*)color(blue)2/3(x+8)#

#color(blue)(3*)(x+6)=color(blue)(color(red)cancelcolor(blue)3*)color(blue)2/color(red)cancelcolor(black)3(x+8)#

#color(blue)3*(x+6)=color(blue)2*(x+8)#

#color(blue)3x+color(blue)3*6=color(blue)2x+color(blue)2*8#

#color(blue)3x+color(blue)18=color(blue)2x+color(blue)16#

Now, subtract #2x# from both sides, then #18#:

#3x+18=2x+16#

#3x+18color(blue)-color(blue)(2x)=2x+16color(blue)-color(blue)(2x)#

#3xcolor(blue)-color(blue)(2x)+18=2x-color(blue)(2x)+16#

#x+18=color(red)cancelcolor(black)(2x-color(blue)(2x))+16#

#x+18=16#

#x+18color(blue)-color(blue)18=16color(blue)-color(blue)18#

#xcolor(red)cancelcolor(black)(+18color(blue)-color(blue)18)=16color(blue)-color(blue)18#

#x=16-18#

#x=-2#