Question

How do you solve `\frac { 1} { 3} - \frac { x - 2} { 10} = \frac { 3- 2x } { 15} - \frac { 1} { 6} + x`?

Answer 1

`x=15/29`

Refer to the explanation for the process.

Explanation:

Solve:

`1/3-(x-2)/10=(3-2x)/15-1/6+x`

Determine least common denominator (LCD):

`3:` `3,6,9,12,15,18,21,24,27,color(red)(30),36...`
`6:` `6,12,18,24,color(red)30..`
`10:` `10,20,color(red)30...`
`15:` `15,color(red)30...`

The LCD is `30`.

Multiply both sides by the LCD `30`.

`(30xx1/3)-(30xx(x-2)/10)=(30xx(3-2x)/15)-(30xx1/6)+(30xx x)`

`(color(red)cancel(color(black)(30))^10xx1/color(red)cancel(color(black)(3^1)))-(color(red)cancel(color(black)(30))^3xx(x-2)/color(red)cancel(color(black)(10))^1)=(color(red)cancel(color(black)(30))^2xx(3-2x)/color(red)cancel(color(black)(15))^1)-(color(red)cancel(color(black)(30))^5xx1/color(red)cancel(color(black)(6))^1)+(30xx x)`

Simplify.

`10-3(x-2)=2(3-2x)-5+30x`

Expand.

`10-3x+6=6-4x-5+30x`

Simplify.

`-3x+16=1+26x`

Add `3x` to both sides.

`-3x+16=1+26x`

`16=1+26x+3x`

Simplify.

`16=1+29x`

Subtract `1` from both sides.

`16-1=29x`

Simplify.

`15=29x`

Divide both sides by `29`.

`15/29=x`

Switch sides.

`x=15/29`