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

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Answer 1 · 2018-03-07T04:17:48

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 $x$ :

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

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

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

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

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

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

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

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

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

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

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

$3x+18=2x+16$

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

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

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

$x+18=16$

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

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

$x=16-18$

$x=-2$

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