Question

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

Answer 1

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`