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

Question

Ethan Adkins · Accepted Answer

The solution is #x=-2#.

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)# The formula for color(blue) is 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#

Julia Adams · Answer

undefined To solve the equation $ \frac{1}{4}(x + 6) = \frac{1}{6}(x + 8) $, you can follow these steps:

1. Multiply both sides of the equation by the least common denominator, which is 12.
2. Distribute the terms inside the parentheses.
3. Solve for $x$.

The solution is $x = 9$.